The problem is, that by stating that, you now incentivize people back to "searching every square", just with words. I search the room, find anything? Okay, I search... the statue, the bed, and the bookshelf. Still no? Okay, let's get specific, I check out the statue's eyes and hands, underneath the bed and in the mattress, and behind the bookshelf and on the shelf that starts with the letter H, cause Halaster was crazy like that."
This is a playstyle issue, and really goes back to Mearls thesis that you can't make a DM better through the rules. In this instance, it applies to the players also.
Ideally, I think a room should be divided into a number of zones (the floor, the walls, that closet, the statue). If there are any interesting features to be found in the room, the description should indicate specifically what these are ("the statue's teeth slide inwards").
A DC (or rank, whatever) should be given for things assuming Passive Perception - if the PCs wander through the room, they may see some things automatically.
If the players say "we search the room", they should roll Perception against those same DCs.
If the players get more specific ("we search the statue"), they should roll Perception with a hefty bonus (+5, or with a 'rank' bonus) - but only for features in that 'zone'.
And if the players happen to hit the right words ("we check the statue's teeth"), they should find any appropriate features automatically.
But if there is a feature in that same zone that is not in the specific area they described, they should
still get a roll for searching the whole zone. (That is, if they say, "We check to see if the statue's arms move", they should get the roll for searching the statue 'zone. If that roll was a success, the DM should say, "The arms don't move. However, as you search you do notice that the teeth appear loose...")
(It may also be wise to differentiate between things that can be found by simple observation, and things that require the PCs to interact with the object being searched. Just in case of contact poisons and the like.

)
The game should also give strong advice to the DM not to insist on pixel-bitching - Perception rolls are related to broad zones, not single specific features. The game should also strongly advise
players not to bog play down by overdoing their searches and, perhaps more importantly, should also advise the DM not to allow multiple searches in the same zone - once they've rolled for the statue, any further detailed questions should meet with the response, "you've already searched the statue, and didn't find anything."
(This must apply even if their second, more detailed search happens to hit exactly the right spot. I guess they're just too close now to see it. This last is actually really crucial - otherwise you're still liable to get the ever-more-detailed search problem.)
Beyond that, I don't think there's really anything the game can do. If the DM is going to insist on pixel-bitching, the rulebooks can't stop him. If the players are going to insist on searching every inch of the game world in detail, the rulebooks can't stop that either.
Oh, one more thing: DM's (and adventure designers)
must learn to be content with PCs not finding every secret in the game. If there's a secret door, it may well go unfound, and that's just the way it is. Otherwise, there's no point in bothering with Perception skills (or secret doors, or whatever) at all - if the DM insists that the PCs find these things anyway, they're better off just telling the players about them outright.