After everybody has gathered to fight Bahumut Sin, they are all on or near the ground. This is followed by a short scene lasting no more than a minute. Cloud then proceeds to jump up the tower, aided along the way by his companions, all of whom were stood around him on the ground only seconds previously.
During the bike chase sequence, Kadaj bursts through a barrier reading: "WARNING: Authorized Parsonal Only." "Personnel" is the correct spelling. This error only appears in the original version, and is corrected in Advent Children Complete.
During Sephiroth's opening monologue before he and Cloud begin to fight, when he says "What I want, Cloud...", you can see through his hair to his earlobe, where his hair should be thicker and you shouldn't be able to see the part of his ear that it covers.
The goof item below may give away important plot points.
Immediately before the fight with Sephiroth begins, Kadaj drops his sword, making it land several hundred feet beneath him. He subsequently turns into Sephiroth, and fights Cloud. At the end of that fight, when he becomes Kadaj again, he has mysteriously recovered his sword and uses it to attack Cloud. Also, when falling to the ground, his sword is facing forward as Sephiroth held it, when he lands, it is backwards, as Kadaj holds it.