If four PCs enter a room, can they all do perception checks in a row to improve their odds of detecting stuff?
If the party must make Perception checks when entering an area, the party should make Perception checks simultaneously
If everyone enters the area at once, everyone makes individual Perception checks simultaneously because everyone entered the area at once. Having one PC bust open the door while the other PCs shield their eyes then having each PC open his eyes so that the non-blinded PCs make their initial Perception checks with increasingly larger benefits because of other PCs' aid another actions is brilliant but also incredibly genre-savvy and metagamy. This GM doesn't know if he'd prohibit such a tactic—it does, after all, still carry significant risk—, but he would wonder what he'd done to encourage it.
That is, first, there's no rule that says a Perception check's made upon entering an area, sequentially, simultaneously, or otherwise. Stuff that's in plain sight will just be noticed by the PCs automatically, in the same way that stuff that's odorless, silent, and behind cover won't be by most PCs. The only reason to make a Perception check upon entering a room is if there's stuff in between these extremes—something concealed, inobvious, or requiring further inspection to understand. For example, an invisible monster in a room warrants a Perception check upon opening a door, but an ornate fountain or wheel of Stilton in the middle of the room wouldn't; the wheel of Stilton might require further inspection to notice it's attached to giant mousetrap, but no amount of listening or staring will reveal the odorless ingested poison in the fountain's water.
Second, it's okay for PCs when they aren't in danger or distracted to take 10 on Perception checks, and, much of the time they can even take 20. A stress-free, seemingly safe room really should enable all the Perception checks the PCs want to make.
In sum, PCs need only roll their (simultaneous not sequential) one Perception check when something dangerous or distracting's in the area or time is of the essence. If there's nothing dangerous or distracting and the PCs are unwilling to spend 2 min. per square to take 20, let them take 10 and move on.
This might be disconcerting because it makes old-school, stumble-into-them style traps less dangerous. If there's a trap you really want to use, there's this question, but traps are often low-level threats that PCs outgrow, and a group that recognizes that the game's most important skill is Perception won't have any problems detecting traps anyway unless they're put in dangerous or distracting situations forcing them to roll. In other words, the dungeon's a lot more dangerous with monsters about.
Rules as written does allow everyone to make that check, but it slows the game down and ruins things. The way my group does most checks like this is the person present who has the best skill makes the check, and if one other wants to assist then they can.