In some cut-scenes, Sora's Keyblade changes back to the original Kingdom Key he starts out with, even when the player is using a different one.
During the Pegasus Cup, it goes from the 4th Seed, straight to the 2nd Seed, missing out the 3rd.
When Riku throws the board down on the beach, for the raft, it vanishes in the next shot.
Before the fight with the pot barrel spider/centipede boss in Agrabah, after Iago steals the lamp from Aladdin he lands on Jafar's left shoulder. After Jafar says, "Attack," there is a cut and Iago is no longer there.
Whenever any characters come back from being completely underwater, they are never wet.
When Sora and the gang return to confront Cerebus in the Colosseum (when Hercules rescues Cloud), you can see Sora's keyblade pass through Goofy's shield.
In Hollow Bastion, right after you defeat the Maleficent Dragon and before you fight Riku/Ansem, during the movie scene where Sora sees Kairi on the ground in front of the keyhole in the hall containing the Princesses of Heart, Sora lifts Kairi and shakes her up and down to wake her up. The pendant on Kairi's necklace stays suspended in the air when he shakes her until the shot changes.
When using the Gummi Ship for the first time, Goofy warns Sora that 'the Heartless ships often give us a hard time. However, he and Donald have only just learned who the Heartless are - leaving Traverse Town is their first Gummi Ship journey since then. Ergo, they have no way of knowing that these enemy ships are Heartless (except having just figured it out, but Goofy acts like it's common knowledge to them that these are Heartless).
The Clock Tower in Neverland (the Big Ben in London) is considered part of the world of Neverland itself, even housing Neverland's Keyhole, although it is clearly a separate world within the context of the Peter Pan (1953) story.