Since you mentioned mage spells, I will answer in a mage's perspective.
In short: Use more cantrips, and adapt to the situation. Most of all, cooperate.
Use more cantrips
1. How can a mage learn new cantrips after character creation?
Since cantrips are spells, and the mage can add two new spells to his or her spellbook each level, a mage can choose cantrips for these spells. Likewise, the mage could copy a cantrip off of a scroll, if one exists, or out of another wizard’s spellbook. The mage can obtain new cantrips just like he or she gains new spells of 1st level or higher.
(Source: D&D Next Q&A: 10/10/13.)
RAW, you have no limit on how many cantrips you can learn. The rules just state that you start with three cantrips initially, and it is not a hard limit. Sure, cantrips can only produce negligible effects compared to spells with levels, but your character (and probably yourself, because you have gone through all the burden to play a spellcaster) is smart, and a smart person like that can surely make creative use of mere cantrips. For example,
- Dancing lights can be a good warning signal to your allies.
- With mage hand, you can deliver all the good spells like mage armor to your comrades.
- Mending can be used to fix a mundane item with minor flaws. Good for roleplaying.
Of course, you can instead do offense with cantrips and prepare more leveled spells for utility. For instance, aside from dealing damage, ray of frost also slows the opponent. This effectively prevents him from coming through the battlefield and cutting weak party members while your meat shield is holding him off.
Campaign-dependent: Reduce your need for spells by obtaining proper items
For example, with Elven Chain and other party members having decent AC, you wouldn't have to prepare mage armor, because your AC is already equal to what mage armor can provide, and probably you are the one with the lowest AC in the party. Likewise, proper magic items can reduce the need of certain spells, or something like Ioun Stones can even remedy the situation immediately. Of course, this is campaign-dependent because loot is entirely dependent on your DM's discretion.
If you are that desperate, then multiclass
If everything fails, there is always the final place for refugee: Multiclassing. Taking a dip in another spellcasting class will net more kinds of low-level spells in your reservoire. (Also note that some spells like cure wounds can be actually cast at higher levels even if you have only one level on the class which gives it, RAW.) Taking a dip in a class with heavy armor proficiency will virtually remove your need for mage armor. Of course, you lose awesome features of a high-level mage, but if you badly need more spells (or less trivial spells), then you should give it a try.
Don't try to do everything
If you are not soloing, you will probably have other party members, and I suppose one of them will be another spellcaster. Talk with her. Unless she is an offense-oriented hybrid caster like a paladin, probably your area and her area will overlap. Debate with her, and fix your role. You can save your grease when your druid friend will instead cast entangle for you.
Post Script: DON'T mind the levels
Even you have admitted that spell levels are less relevent in D&D Next. In 3.PF, hold person is inferior to hold monster even if you use it to a person, because lower-level spells actually have lower save DCs. However, in Next, they have the same save DCs, so hold monster is only truly effective against non-humanoids. Also, some spells can be cast on a higher level for stronger effects. For example, magic weapon gets its enhancement bonus upgraded when cast with higher level slots. Do not think the spells as "Nth-level defense/offense/utility". Rather, mind the roles of the spells. If you prepared grease to abruptly stop enemies and ray of enfeeblement to weaken the brute coming, that's fine. If you prepared them just to fill "1st-level offense" and "2nd-level offense", don't. By regarding the spells as roles instead of levels and categories, you'll find out that there is actually much space to squeeze in your daily preparation limit.
I have to agree that the wording in the original rules is not a 100% explicit. It is clear that you cannot cast spells of a higher level than you have access to, but can you prepare them? The Pathfinder FAQ has a more complete answer, emphasis mine:
No. You only get the bonus spells if your class level grants you
access to those spell levels. You can't even use them for lower-level
spells. See page 16, Abilities and Spellcasters section: "In addition
to having a high ability score, a spellcaster must be of a high enough
class level to be able to cast spells of a given spell level. "
For example, a 1st-level wizard with 18 Intelligence has (according to
table 1–3: Ability Modifiers and Bonus Spells) 1 bonus spell at spell
levels 1, 2, and 3. However, he can only use the 1st-level bonus spell
because as a 1st-level wizard he only has access to 1st-level spells
(his class-based number of 2nd- and 3rd-level spells per day are "—",
meaning "no access to spells of this level"). As soon as he becomes a
3rd-level wizard, he gains access to his 2nd-level spell slots and can
use that bonus 2nd-level spell slot from his high Intelligence, and
likewise for 3rd-level spells and bonus spells at wizard level 5.
Basically, ignore the columns for higher-level spells on table 1–3:
Ability Modifiers and Bonus Spells until your class grants you access
to those spell levels.
The Pathfinder FAQ is considered official in the Paizo community and is binding for Pathfinder Society (http://paizo.com/pathfinderSociety/faq#v5748eaic9qy5).
Best Answer
Yes, he can.
As per PFSRD,
There is no obligation to drop those extra prepared spells; moreover, you could change your selection of additional spells prepared (but not the selection of spell slots they are in).
As a side note, a scroll or wand of Mnemonic Enhancer (or, rather, the retain option of the spell) would not be terribly effective, since you must cast it on the round following the casting of the spell you wish to retain.