Yes, its possible for there to be more than one valid hash. I don't know what the mathematical probability of this is, but if you were to exhaust the entire nonce spectrum, there are likely to be several valid blocks. Most blocks, however, stop when they get a valid hash, so it seldom is an issue. Though occasionally, two miners might come up with different valid hashes at the same time, and this results in one of them being rejected.
As for a collision, well, that's effectively impossible. First, yes, it's possible that the same hash could be found for two different blocks, but that's not a collision. It's also highly unlikely. Unlikely to the point of there being no point in dealing with it.
Yes, it could screw up certain software that assumes hashes are indexable and unique, but it shouldn't really be an issue for the blockchain itself to have duplicate hashes.
The only real "collision" would be if an attacker were trying to come up with his own block of transactions, with the same parent that would somehow hash to the same value and trying to "take over" the other block, and that is astronomically unlikely to the point of absurdity.