Continuity mistake: When Eric's boat leaves with Ursula in, there are ribbons and a long piece of fabric decorating the side of the boat by the 2 portholes, which disappear in later shots.
Sacha
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.
Sacha 
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.
Sacha 
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.
Sacha 
Continuity mistake: Eric's statue changes between shots, notice the position of the right fist.
Sacha Continuity mistake: When the storm breaks, the ship's look-out appears/ disappears randomly between shots.
Sacha Continuity mistake: When Ariel is peeping on the boat, Max licks her face and you can see that the rope next to the window disappears behind a beam. After Eric sees his statue, the rope is now really long and is laying on the deck, forming a big circle.
Sacha Continuity mistake: When the movie starts, the big lamp is lit, yet when Triton arrives to light it with his magic trident, it suddenly appears unlit.
Sacha Continuity mistake: When Scuttle peeps on the porthole and discovers Ursula, the design of the porthole changes style between the first and last shot.
Sacha Continuity mistake: When Ursula and Eric's boat sails away, people suddenly appear on the left side of the boat.
Sacha Continuity mistake: When Grimsby discovers his crab is gone, little footprints have magically appeared on the table.
Sacha Continuity mistake: When Ariel refuses the eels' help, before they toss the face of the statue, she lowers her head and cries. A frame later the head is tilted to the right.
Sacha Continuity mistake: When the song 'Under the sea' begins, Ariel is sitting on a rock. The amount of purple flowers on the sides, specially on the right side, change drastically between shots: They appear, disappear, reappear, change flowers, then to algae.
Sacha Continuity mistake: When Ariel first sees the fireworks, they are coming from the boat, but when the angle changes and the boat has moved along, they are being fired from the same spot, though now it's set in the middle of the sea, which is absurd. Some animator screwed it badly.
Sacha Continuity mistake: When Sebastian escapes from the dip, the sauce has a white colour. When he throws the bowl over Louis' head it's changed to brown colour.
Sacha Continuity mistake: After the shipwreck, when Ariel sings, moss suddenly appears on the rock right below her hands.
Sacha Continuity mistake: Eric's ship sails swap from plain to striped when the storm breaks.
Sacha Continuity mistake: During the Sebastian and Louis scene in the kitchen, all the stuff on the tables around keeps changing (appearing, disappearing, reappearing) between shots, with no logic whatsoever.
Sacha Continuity mistake: When Flounder guides Ariel to the sunken statue of Eric, the statue's visage and position change drastically at least 3 times during the scene.
Sacha Continuity mistake: The first time we see Eric's boat, the number of lamps on the stern decreases between shots.
Sacha 
Answer: Yet another Disney urban legend.
Jazetopher