Continuity mistake: The FMV/cutscene in Besaid, the one after the first time you talk to Yuna and then talk to Wakka to get some rest, has the position of Tidus in the wrong place. He awakens in the "Crusaders Lodge" however the cutscene takes place across from the lodge in Wakka's hut. The cutscene ends and you are back in the Crusaders Lodge. This can be seen as the temple arches are coming from the right side of the screen and you can see the Crusaders Lodge behind Lulu, where Tidus is supposed to be peaking out of.
Audio problem: In the scene where Tidus and Yuna are conversing at the Farplane, Yuna says something slightly offensive about Tidus' mother, to which he replies, "Whoa there, that's my mother you're talking about!" Almost immediately after, you hear Yuna say, "oh, I'm sorry," but her mouth doesn't move.
Continuity mistake: When Tidus is teaching Yuna how to whistle and says "Put your fingers in your mouth like this," he talks as if he has his fingers already in his mouth for the entire line when he doesn't actually have them in his mouth until he says the last two words.