Continuity mistake: During the "Kiss the Girl" song a bunch of fish swim up underneath the boat, and the water is seen to be very deep. After the boat is knocked over however, Ariel and Eric are standing in the water which now appears to be only a few feet deep.
Continuity mistake: When Sebastian is in Ariel's cavern with all her treasures, he accidentally gets his legs caught in a thimble. You can see it from the front, but when they show a shot from the back, it is gone. In the following shot from the front, it is back on again.
Continuity mistake: When Ariel is crying and Sebastian comes to comfort her, there's a vase, two planks and a small bottle behind her. When the angle changes, every object is different, even the area looks much wider.
Revealing mistake: When we first see Max, his paws are leaning on a balustrade and become transparent. Though it may seem like it's an optical effect because they're in the shadows, the next angle shows them fully lit and opaque.
Continuity mistake: When Ariel spies the guys on the boat, she is under an arched window. Depending on the angle, the space is made of 3 blocks of wood, or 2. This keeps changing randomly all the time.
Continuity mistake: During the eels scene, when Ariel is crying, the stone she lays on is a single stone laying almost flat on the sand; then swaps to a double stone, and when she sends the eels away it is a single stone though way steeper, standing upright.