Continuity mistake: When Chip fires up Maurice's invention and rides toward the cellar, in the shot facing the cottage we see there's nothing in the cellar handles, but in the closeup as Maurice's machine hacks away at the cellar doors there's a long branch inserted in the handles preventing the doors from opening.
Continuity mistake: When the Beast shows Belle to her room and then says she will join him for dinner before shutting the door, Belle is wearing her cloak. She's still wearing it when she runs over to the bed, kneels down and starts crying. When we see her again (after the Gaston scene which is in-between), she's no longer wearing the cloak, and she couldn't have removed it at any point because her position next to the bed hasn't changed since she started crying and she doesn't move again until Mrs Potts taps on the door to offer her a cup of tea.
Continuity mistake: When the Beast shows Belle to her room, in a wideshot you can see the oval centrepiece of the foot of the bed has a large purple rose painted on it and it has a plain red border. In a later scene after Mrs. Potts and Chip leave Belle's room, the purple rose and red border have vanished from the centrepiece, which is now only decorated with evenly spaced gold dots. (00:24:35 - 00:31:05)
Continuity mistake: When Gaston is telling Belle all she has to do is marry him, and her father will be let go from the asylum, his hands are bare. Then when Belle gets the magic mirror and cries "Show me the Beast!", Gaston has yellow gloves on. Then in the next shot they're gone again. (01:07:25)
Continuity mistake: In the scene where Belle first comes to the gate castle to find her father's hat, she pushes the left side of the gate that's already partly open. But when her father came, he opened the right side of the gate and slammed it shut. How did the left side of the gate open? (00:20:05)
Continuity mistake: In the beginning of the movie, Gaston is using a blunderbuss (early rifle) to shoot the birds. He also has a quiver of arrows on his back. But he doesn't have a bow until the end of the movie.
Continuity mistake: After Chip taps the spoon its position changes between shots.
Continuity mistake: During the fight scene at the end, knives are thrown at the villagers. Nobody is hit, but three knives get stuck in the left kitchen door. The villagers open both kitchen doors and, from the inside of the kitchen door, there are only two knives, each stuck in the right kitchen door.
Audio problem: Maurice's machine starts working and one of the logs hits him with a 'thunk', yet the sound of the log hitting the ground is never heard.