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.
Factual error: After Ariel is changed into a human, she swims frantically to the surface for air, and when she comes up she does the magnificent throwing her head back and splashing water everywhere - we've all seen it. But this would mean she would have to actually tilt her head further down in the water before breaking the surface, so she could then throw it back- something that makes no sense for a person who's about to drown, and wants air as soon as possible. Can't have been a "hair in face" problem - her hair was streaming out behind her underwater, so wouldn't have been in the way if she'd broken the surface face first.
Factual error: At the end of the film, when Ursula has Triton's powers, she creates an enormous whirlpool that pulls wrecked ships off the ocean's floor. Prince Eric boards one of the ships that is being swept along with the whirlpool's currents, then turns the rudder hard to steer the ship into Ursula. Not possible - in order for the rudder to change the course of a ship the vessel must be moving faster than the current.
Continuity mistake: When Ariel and Flounder are going into the shipwreck at the start, Ariel goes through the porthole and Flounder follows. In the frame where he gets stuck, his front fins are trapped firmly outside the porthole but in the next shot inside the boat, they appear inside instead of outside.
Continuity mistake: In the scene when Ariel saves Eric after the ship has exploded he has boots on yet when Ariel has brought him up onto shore they are off, they couldn't have fallen off since they in that time period men wore boots that have to be taken off to at least to the heal and Ariel is tying to save him so she wouldn't take the time to get them off, and leather tends to tighten up when thoroughly soaked so that is another factor to why they shouldn't have come off this also happens at the end of the film after Ursula has been killed.
Continuity mistake: When Ariel goes to the surface to show Scuttle the fork, he first sees her through the telescope (which is the wrong way round). When you see Ariel through the telescope, she appears to be surrounded by the sea but when Scuttle takes away the telescope she is close up and right next to the rock he is on. Surely the rock would have seen through the telescope underneath Ariel not ocean.
Factual error: When Louis the chef starts to sing he mentions typical French things like "Maurice Chevalier", a french actor who became very famous as of the 1920's. Though the movie is timeless, the clothes and lifestyle (pirates, ships, horse carriages) set it long before the 20th and even the 19th century.