Passive Investigation could be a way to determine whether to feed players information that their character might pick up on, but the player might not think to explicitly ask. Note that a passive check can be against a DC, rather than an opposed roll. Some examples:
- From the angle of the body, it looks like the Mayor didn't fall... She was pushed!
- That pouch looks awfully light to be containing 300 gp.
- Isn't it odd that the Kobold only steps on every third white tile?
How are these things not Perception? Because what you are noticing isn't remarkable unless you compare it to your expectation of how things should be. It's a test of reasoning rather than of, well, perception. I keep wanting to say "think Sherlock Holmes", but he's also rocking Perception, so that's actually a terrible example. So... Rain Man, maybe?
PHB suggests passive checks (p 175) where the GM doesn't want the players to know they've succeeded or (more typically) failed at something.
A passive check is a special kind of ability check that doesn't involve any die rolls. Such a check can represent the average result for a task done repeatedly, such as searching for secret doors over and over again, or can be used when the DM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster....
Hidden checks are fun:
- Arcana to see whether you realize the mystic sigils on the amulet you're buying are all inverted
- Animal Handling to determine whether the donkey will kick you as soon as it sees an opening
- Deception for whether an unseen observer notices you slip out of your false identity when you think no one is noticing
A paranoid player might call for a check for all of these things, but if they don't think to, they won't know they failed until you start giggling.
Short answer
Yes, the Observant feat helps a character only when they are not actively looking. It is possible to make sense of this in terms of how active Perception is framed by the rules, and with reference to real-world ideas about the conscious and unconscious mind. The +5 bonus only applies to Perception/Investigation skills when used passively, but it is still possible to exceed this score ("notice more") with active Perception/Investigation by rolling 16 or more.
Long answer
As the introduction to feats in the PHB says (my emphasis):
A feat represents a talent or an area of expertise that gives a character special capabilities. (PHB 165)
The talent/special capability which the Observant feat gives is that you are:
Quick to notice details of your environment (PHB 168)
This is different to an active Perception check, where you mostly have to specify exactly where you are looking to have any chance to find anything.
In most cases, you need to describe where you are looking in order for the DM to determine your chance of success. For example, a key is hidden beneath a set of folded clothes in the top drawer of a bureau. If you tell the DM that you pace around the room, looking at the walls and furniture for clues, you have no chance of finding the key, regardless of your Wisdom (Perception) check result. You would have to specify that you were opening the drawers or searching the bureau in order to have any chance of success. (PHB 178)
I can think of two reasons why it makes sense that the Observant feat only benefits passive Perception. The first is based on the wording of the rules, and the second on my basic understanding of psychology.
- Observant will only work with things which are potentially noticeable in the immediate 'environment', ie not more narrowly specified locations (this is the purview of active Perception)
- You could understand passive Perception as being what the unconscious mind sees, and active Perception as being what can be uncovered by the conscious mind.
You can take or leave the last point, as not everyone subscribes to this psychological model.
I've argued here from the point of view of Perception, but the same ideas can be applied to active and passive Investigation, which the Observant feat also covers.
In any case, this does not mean that your character's passive Perception/Investigation scores are always "better than the active ones", as the die roll could be 16-20, which would take you above your passive score, but the bonus only applies to passive checks for the reasons given. Of course, you could also roll lower, but even without the Observant feat, it is possible to roll better, worse or the same as your passive Perception/Investigation, and the feat just raises the bar of your passive scores.
Best Answer
Nothing prevents this.
Multiple instances of advantage don't stack. But that's not what's happening here. Observant increases your passive perception and investigation by +5, period. This means it can be affected by advantage.
So Dungeon Delver grants you advantage (+5 to passive), effectively resulting in a +10 passive bonus overall.
So your base perception would be, when searching for secret doors passively, 20 + WIS.