Continuity mistake: When King Triton destroys the stone statue of Prince Eric, you can clearly see that the statue's face explodes and breaks into pieces as well as the rest of the body. However, at the point a few minutes later when Ariel decides to meet the seawitch Ursula, she caresses the statue's face as a whole again.
Continuity mistake: When the wedding is taking place, the priest's cross turns upside down for one frame.
Continuity mistake: When Sebastian is hiding from the chef under a lettuce leaf in the kitchen, at first he is behind a bunch of stuff on the table. In the next shot, all the stuff is gone, and he's alone on the table.
Continuity mistake: When Flounder swims through an anchor at the start the anchor has round edges, but when the shark bursts in the anchor has flat edges.