1. In the big underwater concert scene at the begining of the movie, a long shot of the concert hall shows the chandelier brightly lit. Then, when King Triton swoops in, the chandelier is dark, without having been turned on. He then lights it with his trident and everyone applauds as though the newly-lit chandelier is impressive, even though it was already alight just moments before.
2. Right after Ariel sings "Part of Your World" in her treasure cave, Sebastian falls down a couple of shelves and gets tangled in some of her collection. When he is shown face on, he had a thimble stuck on his right rear leg. However, when they show him from behind, the thimble is gone! This happens a couple of times as the scene shifts between the two views.