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.
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.