You can use spellcraft to identify a spell as it is being cast. But does this check let you know the target of the spell? As an example of when this could matter quite a lot, Dominate allows you to control someone telepathically. You'll really want to know who the evil wizard just tried to dominate!
The rules (3.5/PF) do mention that
You make all pertinent decisions about a spell (range, target, area, effect, version, and so forth) when the spell comes into effect,
so clearly for spells with a longer casting time, you can't know the target until the very end.
I believe the RAW are simply silent on this issue (certainly the spellcraft skill itself provides only minimal guidance) but I'm wondering if there's something I've missed. Also, I chose target for concreteness, but the situation in general applies to each of the "decisions" mentioned above.