So, I don't remember for certain, but I think I remember that you can fire a ranged weapon/do a melee attack at a square instead of at an enemy? How does that work? And besides against Invisible enemies, when is it useful?
Ranged attacks against square are useful when using splash weapon (or maybe intersections of squares, I don't recall RAW rule on this - personally I allowed targeting specific square with splash weapon but it might be house-ruling).
Yeah, you have to target the intersection typically. If you target the center of a square that you know a creature is in, you are considered to actually targeting the creature (this also includes "intersections" covered by larger creatures).
Other than that, its main use is to try and target invisible creatures.
Though if you have an a-retentive DM that won't let you fight defensively for the round (so you can still make AoO but gain some of the AC bonus), because you didn't make an attack. You could always claiming, "I think there might be an invisible creature in this square next to me. I attack the square. Oh, I don't hit anything there. Well I guess I get the fighting defensively dodge bonus anyway."
Personally I think that is stupid, so I allow my players to spend a standard action to gain the fighting defensively dodge bonus (and attack penalty) if they don't attack anything that round.
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If you're talking about targetting the floor of a particular square, the AC of the floor is 5. You shouldn't need to roll to hit against a section of floor you occupy or one that is adjacent to you, but you might if it's somehow concealed. You'd typically do this if you're firing or throwing something to make that square impassable or difficult to move through or when you have something like a smoke grenade you want to burst at a creature's feet.
Attacking the floor is also a good idea when you suspect it may be weak and likely to fall through under an opponent.
You could also close your eyes and attack the square where the mirror imaged wizard is to negate the spell effect.
At least according to some in the long threads discussing this.