Important thing to remember: Invisible does not mean formless or lacking mass.

This sort of issue with mundane ways to find invisible creatures and objects has existed since Tabletop games have begun.

Want a simple, low cost (but increasing time cost depending on the area that needs to be searched)?

Flour.

Thats right, your common baking ingredient can foil invisibility (Though in combat it usually only aids in helping mark a target until they move/remove the flour. You still take fighting a concealed enemy penalties.)

If anyone wishes to rules lawyer you because they want to force you to use magic in a no magic zone keep in mind the following:

• You are a fighter
• Mundane can beat magical
• Invisibility is not a world altering spell, nor is greater invisibility. It only affects sight
• The object still possesses mass and thus occupies space
• The flour must do one of the following on contact: show an outline of the invisible object or hide the flour. It cannot allow the flour to pass through without the item being mass-less (and then you would have an entrely different issue. How does one grab what does not exist)

Is spreading any sort of substance around going to necessarily be the cleanest way to do something in a social situation? No, thats where good ROLEPLAY in a ROLEPLAYING game comes in handy. Perhaps you pose as someone important who likes his snuff box despite being "highly allergic". Or wear elaborate clothes with plenty of room. Hell, hide it in a powdered wig. Or use the powdered wig. Use dancing streamers (less effective but they are long and can still touch an object an alter course, you just have to be paying attention.) Be the bumbling drunk using people themselves as your quick senses. Or get creative and use all or more of the same concept ideas.

Course you can always take the base concept (item has mass even if invisible) and run wild. Filling a mansion with water is a great way to make a splash. (invisible object will appear as a pocket of air)

Can you dispel a magic effect you can't perceive?

Yes, as long as you can locate it somehow. If you can't find it somehow, then no. This reduces down to the related question: Can you target a target that you can't perceive? And the answer to that is a qualified yes. Yes, if you can land your dispel magic on the desired target somehow.

As we'll see, your example situations don't allow you cast the spell yet, because you haven't targeted anything. But first, let's look more at how targeting works.

Targeting spells

To target something, you need two things per Targets on PHB page 204 (unless the spell's own description lifts one of these, or adds new requirements):

1. The ability to choose the target

   A typical spell requires you to pick one or more targets to be affected by the spell's magic.

   And dispel magic does require the ability to pick the individual target:

   Choose one creature, object, or magical effect within range

2. A clear path to the target

   To target something, you must have a clear path to it, so it can't be behind total cover.

   This isn't a problem in either situation you're asking about.

So in order to target something, you need to be able to individually choose it. To be able to do that, you need to know that it's there and where specifically it is. You often gain that information by sight, but sight is not required, only knowing the location of your target is required. This information can be gained by many other means: hearing, touch, divination magic, etc.

Now, about that qualified “yes” above: can you target something you can't perceive at all? Only if you have enough knowledge from something other than perception in order to correctly target it.

• For example, if a god granted you divine intervention and whispered in your ear to say “the invisible wizard is hiding behind the third barrel in the south-east corner!”, then you'd be able to target that invisible wizard without needing to use a perception ability of your own. This choice would be “I target the invisible wizard right there, behind that barrel.”

• As another example, if you had a note from a wizard that said, “cast dispel magic on the centre of the wall between the 11th and 12th statues on the left of the entry hallway of the Grand Palace”, that's enough knowledge to correctly target your spell at the illusion the wizard put in that exact location and reveal the secret door (or whatever is there). This choice would be “I stand in front of the wall between the two statues, and I target the magical effect that is right in front of me.”

Other than unusual help like that though, you generally need to be able to locate your desired target, which will almost always require some kind of perception on your part. We can't literally require “perception” in all cases though, because being too literal about that though would rule out some cases like the above where you obviously know enough to target the spell correctly — and we don't want that. D&D 5e is, after all, supposed to be sensible rather than literal-but-counter-intuitive.

The examples in the question lack targets… so far

So you could target something you can't see, but in the examples, no targets can be selected yet without changing the situation somehow.

Notably, you can't just choose a general type of magical effect and hope it is somewhere in range, because that's not targeting an individual magical effect. Dispel magic is not an area of effect spell! Just like you can't choose a magic missile at “any orcs in the room”, you can't dispel magic “any invisibility effects in the room”. You have to be able to pick a specific target and cast your spell at that target specifically.

That means that in both your examples, you can't just cast the spell at nothing, say “Invisibility, I choose you!”, and have dispel magic find the invisibility effect and dispel them just because it's within range. You didn't pick your target! Instead, in each situation, you have to do some more work to acquire and choose your target:

1. You have to locate the invisible hiding evil wizard somehow; most likely by using Perception checks (but divine intervention would work too). Once you positively acquire the knowledge of the position of the evil wizard, then they can be targeted by dispel magic.

2. You can't can't dispel magic on “any and all invisibility effects in range” because that's not how targeting works — that's not one, as dispel magic requires, that's multiple. You would have to pick one instance of an invisibility effect somewhere specific in the room:

   • Try to detect the presence of invisible things in the room somehow,
   • Then, if there are any, locate one of them specifically somehow,
   • Then target dispel magic at that one magical effect specifically.

Anything else isn't targeting, it's throwing a spell into the wind and hoping it magically does something its description doesn't say it does.