The trick's limited to casters that don't prepare spells

Not dubious and more just not mentioned is that access to the locate city bomb is incredibly limited. Only casters who cast spells without preparation can drop a locate city bomb, and a locate city bomb can't be brewed into a potion, scribed onto a scroll, or put into a wand. That said, if the reader is unsurprised to learn that the locate city bomb is the exclusive province of characters both that are mid-level bards, sorcerers, and other casters that don't prepare spells and that have access to either the bard, sorcerer, or ranger spell list, then the reader should skip to this answer's Issues section.

The locate city bomb the question describes requires that the 1st-level Sor/Wiz spell locate city [div] (Races of Destiny 166) be modified by the metamagic feat Flash Frost Spell (Player's Handbook II 91). That metamagic feat can be applied "only to spells that have the cold descriptor." When it's prepared, the spell locate city doesn't have the descriptor cold, and it won't gain that descriptor until after to it has been applied the benefit of the general feat Snowcasting (Frostburn 50), and that feat's benefit applies when the spell's cast not prepared.

Thus the typical prepared caster can't prepare a flash frost locate city spell. (If he could, the spell would typically occupy a 2nd-level spell slot as the "flash frost spell uses up a spell slot one level higher than the spell’s actual level.") By extension this means that the typical prepared caster also can't prepare the locate city spell modified by the metamagic feats Born of the Three Thunders (Complete Arcane 76), Energy Substitution (electricity) (Shadowdale: Scouring of the Land 149), and Explosive Spell (CAr 79) so as to make a (potential) bomb. (If a typical prepared caster like a ranger or wizard could prepare in one of his spell slots a locate city bomb, the born of the three thunders explosive energy substitution (electricity) flash frost locate city spell would occupy a 4th-level spell slot, so you know.)

In fact, it seems that of the core classes only bards and sorcerers can cast the locate city bomb as the question describes. The bard or sorcerer takes a move action to collect some nearby snow and takes 1 round (the locate city spell's normal casting time) then 1 full-round action (the extra time a caster that doesn't prepare spells needs to apply one or more metamagic feats' benefits to a spell) to employ the feat Snowcasting while casting the locate city spell modified by the feats Born of the Three Thunders, Energy Substitution (electricity), Explosive Spell, and Flash Frost Spell, the (heavily) modified spell expending one of that sorcerer or bard's precious 4th-level spell slots.

To be clear, at its most basic, this means that a locate city bomb comes from at least a bard 10 (about 1/day) or sorcerer 8 (about 3/day). Also, since neither class receives bonus feats, the trick's game elements marshal every level-up feat the character gained during levels 1–7 plus maybe another feat in the feat Eschew Materials (Player's Handbook 94) as this selection of feats is generally suboptimal if the Snowcasting feat goes unused (see also here). If the bomb—for whatever reason—does not work, that's a lot of wasted effort and resources.

Issues—dubious and otherwise

Below are this writer's immediate concerns with the process the question proposes.

• Does the perfect flash frost spell even exist? The Flash Frost Spell feat in isolation from a rules-as-written perspective is at least mildly dysfunctional. The benefit of the feat Flash Frost Spell "can be applied only to spells… that affect an area" and a spell so modified "deals an extra 2 points of cold damage per level of the spell to all targets in the area" (PH2 91). Most spells that have an area entry don't also have a target or targets entry. None of the spells in the Player's Handbook have both, for example. (While the 2nd-level Sor/Wiz spell shatter [trans] (PH 278) and the 3rd-level druid spell quench [trans] (PH 267–8) both offer the caster a choice between either an area or a target, neither spell has a mode that offers both an area and one or more targets.) Given the game's vastness, there's probably a spell that the feat Flash Frost Spell as written can modify, but finding such a spell won't be effortless, and the spell locate city won't be among them.

  It's entirely possible, however, to read the benefit of the Flash Frost Spell feat's use of the word target as informal, but then what is dealt damage when the feat's applied to the locate city spell? Were a spell that normally deals damage modified by the feat, a reader could discern these informal targets, but as the locate city spell doesn't normally deal damage, the DM must rule what these informal targets are. Any creature in the area? All creature and unattended objects in the area? All creatures, their attended objects, and unattended objects in the area? And so on. The question asks what parts of the locate city bomb need DM adjudication, and this is a point that the DM must address as the Flash Frost Spell feat provides no guidance in this regard.

• What does extra mean? The spell modified by the feat Flash Frost Spell "deals an extra 2 points of cold damage per level of the spell" (PH2 91). There is no formal definition of extra damage when the term is used in this fashion. (The Rules Compendium, for example, consistently uses the term almost exclusively in conjunction with critical hits, a nonstarter here.)

  This makes it unclear if a flash frost locate city spell deals 2 points of damage because the extra damage applies despite the underlying spell dealing no damage or deals no damage precisely because the underlying spell deals no damage. There is, so far as I can tell, no textual support for ∅+X=X besides—and I don't use the term pejoratively—common sense (i.e. adding something to nothing nets something). However, as this is a role-playing, a case can be made for ∅+X=∅. This'll take a minute.

  The Dungeon Master's Guide on Effect of Weapon Size that says, "Weapons that deal less than 1 point of damage have no effect. Once a weapon only deals 1 point of damage, it’s not a weapon if it shrinks further" (28). Thus, for example, a grig ninja can only look forlornly at its sized-for-a-Tiny-creature poisoned +1 flaming shuriken (PH 117, 121) (166 gp 1 sp; 0.025 lbs.). The object, although crafted as a weapon (so it also can't be used instead as an improvised weapon), is—according to the DMG—just not a weapon, and it has no effect. Even were the grig to somehow make an attack with it, no effect—in this DM's opinion—includes things like the ninja's extraordinary ability sudden strike, any poison coating the shuriken, and the magic weapon special ability flaming. Another reader's opinion on the definition of no effect may vary, of course, but I suspect that a DM that tells a player that a monster's attack had no effect then goes on to detail how the PC has been poisoned, level drained, and improved grabbed will be seen as a bit disingenuous.

  The wider view is this: If X can't do Y, then doing Y with X anyway also can't result in Z. For example, when a flash frost locate city spell is cast, because the spell normally doesn't deal any damage, the spell's effect won't generate other effects that're contingent upon the spell dealing damage. Those are just ignored.

  In sum, to this reader, saying that the extra damage from the Flash Frost Spell feat applies to the spell locate city is like asking Pizza Hut to deliver a topping but no pizza: Chances are an intrepid negotiator could buy from a Pizza Hut only a topping just like a determined player could find a DM who'd agree that the +2 points of extra cold damage from the feat Flash Frost Spell can be added to the locate city spell's ∅ damage, but she might have to shop around for an accommodating Pizza Hut or an agreeable DM.

• How do metamagic benefits apply exactly? As previously discussed, there's an absolutely precise order of operations that must be adhered to if a locate city bomb is to be dropped. After realizing the benefit of the feat Snowcasting the caster of the spell locate city then applies on the fly to that spell the following metamagic feats in this exact order: first, the feat Flash Frost Spell that can only be applied to spells that possess the descriptor cold; second, the feat Energy Substitution (electricity) that changes the locate city spell's descriptor from cold to electricity; third, the feat Born of the Three Thunders that can only be applied to a spell that deals electricity or sonic damage and that adds an effect requiring a Reflex saving throw; and, fourth, the feat Explosive Spell that can only be applied to a spell that mandates a Reflex saving throw. If metamagic feats are applied in any other order the bomb is a dud.

  This reader agrees with this fine answer that constant targeting isn't a thing in D&D 3.5. (Also see this answer; I mean, I, like, really agree!) However, when metamagic is applied to a spell, it's unclear if the metamagic benefits apply sequentially in the order the caster prefers or if the benefits apply simultaneously.

  In a totally different context, the sometimes-suspect Main FAQ says that as "a general guideline, whenever the rules don’t stipulate an order of operations… apply them in the order that’s most beneficial to the 'controller' of the effect" (51), but this general guideline is not followed by the only example of the interaction between metamagic feats when their order application matters: the interaction between the feats Empower Spell (PH 93) and Maximize Spell (97–8). The printed benefit of the feat Maximize Spell, in part, says

  An empowered, maximized spell gains the separate benefits of each feat: the maximum result plus one-half the normally rolled result. An empowered, maximized fireball cast by a 15th-level wizard deals points of damage equal to 60 plus one half of 10d6. (ibid.)

  To my knowledge, no other examples exist of how to apply metamagic benefits when the order is actually important, as it is to make a locate city bomb. In other words, for a locate city bomb to go off, the DM must rule that each metamagic feat is applied in the most favorable order.

  If the DM rules that each metamagic feat is applied simultaneously and separately, then the feats Flash Frost Spell and feat Energy Substitution (electricity) find the spell locate city with its descriptor cold from the Snowcasting feat acceptable, but the feats Born of the Three Thunders and Explosive Spell do not find the cold locate city spell acceptable: the cold locate city spell won't be eligible for those feats until after the other feats have been applied to the spell.

  In short, this is a gray area as there is no rule-as-written order of metamagic benefits application—and the DM must rule that order of application favors the bomber for the locate city bomb to work. This general topic, by the way, is rarely broached. I found only a 2013 thread from the Rule of Cool messageboards that reaches some eyebrow-raising conclusions in support of simultaneity and a 2005 thread from Andy Collins's Tapatalk messageboards. (Unfortunately, 3.5 revision architect Collins himself doesn't participate in the latter, but the OP of the former does—in 2013! Small world.)

  (So the reader's aware, besides the locate city bomb the other topic in metamagic application ambiguity is the duration of a spell modified by both the feat Extend Spell (PH 94) and the feat Persistent Spell (CAr 81). Folks apparently die on hills named 24 Hours, 24 Hours Plus Its Normal Duration, 48 Hours, and Would You Guys Keep It Down? We're Trying to Play a Game Here.)

• A circle is a burst? Although he knows he shouldn't be, this reader actually is mildly uncomfortable with the locate city spell's entry Area: 10 miles/level radius circle, centered on you meeting the requirement of the feat Explosive Spell that says that the feat's benefit "can be applied only to spells that… affect an area (a cone, cylinder, line, or burst)" (79). The entry 10 miles/level radius circle, centered on you is an Other area about which that the Player's Handbook says, "A spell can have a unique area, as defined in its description" (PH 176). Like the 2nd-level Sor/Wiz spell locate object [div] (249) and its entry Area: Circle, centered on you, with a radius of 400 ft. + 40 ft./level and the 6th-level Sor/Wiz control weather [trans] (214) and its entry Area: 2-mile-radius circle, centered on you; see text, the spell locate city just doesn't have an area that's a cone, cylinder, line, or burst.

  Technically, it seems that the locate city spell is ineligible on these grounds alone to be the beneficiary of the feat Explosive Spell. (Ironically, as this fine answer mentions, equally ineligible is the 3rd-level Sor/Wiz spell fireball [evoc] (231) that has the entry Area: 20-ft.-radius spread and that has the fact that it's a darn spread mentioned in the example in the benefit of the feat Explosive spell! [Cue groans.])

• "Mission Control, am I ready for launch?" This isn't dubious per se, but it is something to be aware of. The spell locate city possesses the entries Range: 10 miles/level and Area: 10 miles/level radius circle, centered on you. Unlike a normal area spell that has its casters "select the point [within the spell's range entry] where the spell originates" (PH 175), the caster is always the center of the locate city effect. This may mean that, if a caster does manage to drop a locate city bomb, she herself may need a way to avoid the ensuing effect. (The game tends to say so when an effect is centered on the caster yet leaves the caster unaffected; cf. the safe-for-the-caster 3rd-level Sor/Wiz spell fireburst [evoc] (SpC 93) et al. and the your-psion-has-acid-resistance-right? 6th-level psion/wilder power breath of the black dragon [psychometabolism] (Expanded Psionics Handbook 81).)

  In other words, a DM that sees a Sor8 drop a locate city bomb may rule that the caster rockets straight up, is dealt 42,240d6 points of damage, and is technically in space. (Also see this question.)

I know that's a lot, but there's a lot here to unpack. Your patience is appreciated. Anyway, to sum up, there are, in my opinion, a few dubious points according to the rules as written, therefore making it so the DM must rule on the following points:

1. Can the benefit of the Flash Frost Spell feat be applied to spells that possess an area entry yet that don't also possess a target entry?
2. When a spell benefits from the feat Flash Frost Spell, is the damage that's a benefit of the feat dealt no matter the spell's normal effect?
3. Are metamagic benefits applied sequentially in the order the recipient chooses?
4. When the game uses the word circle, does it actually mean sphere, and is that sphere also a burst?

If to each of those questions you said Yes, then you can drop a locate city bomb as the question describes. However, then the DM must answer the final question: Will the caster be affected by the spell?

Note: Even if the DM says yes to only #1 and #2, a Sor4 with a Snowcast flash frost locate city spell can take 1 round then a full round action to commit murder on a kingdom scale. Just sayin'. Also I have come to hate the feat Explosive Spell. Seriously, no damage cap? Really?