FFXIII: The whole thing has a fairytale ending. Nobody caves. Not a single one of the playable cast becomes a Cie'th. This would have had a major impact on emotional levels when playing the game and would have been a cruel yet fantastic twist of events to the storyline.

FFXIII-2: The ending itself is a joke.

FFVIII: Time Kompression is the part that irked me, rather than the orphan thing. The orphan thing I could see as vaguely possible at a stretch, but time kompression made no sense to me at all. How could some places be accessable while others were not? This bugged the crap out of me.

There are undoubtedly a lot of other plot points that have bugged me over the years, but from this thread these are the ones that are sticking in my mind.