At the end of the movie as the prince is pulling out Chip's present, he's seen holding it with both hands for a split second. As he hands it down to Chip his left arm, having been under the gift in the first shot, had disappeared from view.
When the Beast enters Belle's cell, he leaves the door open. However, when Forte plays his tunes to bring the castle down, the door is closed and locked.
When Belle is knocked of the ice by Fife, her skates have suddenly turned into shoes when she is on the snow.
During the course of the movie, the character, Fife clearly has four keys/arms, but at the very end of the film, he is seen to clearly to have six keys/arms.
Throughout the film the chip in Chip's cup form switches from left to right.
During the song "Stories" Belle's book is stitched together and we see her holding it in her hands. Viewing it from the back, the binding is in her right hand; unless it's upside down (which it's not, because we can read the writing on the back cover) the spine of the book should be in her left hand.
At the end of the film, when Fife starts playing the piccolo, he is holding it in the wrong direction. It should be sticking out in the opposite direction.
In every shot of Forte's keyboards, the keys do not match the notes, let alone the rhythm of the music. In one shot, every key is pressed at the same time, but the music shows little sign of dissonance.
When Forte introduces himself to Belle in the 2011 widescreen releases, the audio is sort of out of synchronization and there is a slight pause on the footsteps before the camera pans up to Forte. This is absent in the earlier releases.
Chip makes it sound as if he's never experienced a Christmas before, though we see him in flashback (human form) celebrating Christmas Eve with the castle staff. He was already at least five years old when he was enchanted.
When the Beast says to Belle in the dungeon "You said you'd never leave!" He is seen wearing his blue dance suit but in the next shot when he says "You Broke Your Word and For That you'll rot in this dungeon forever!" He is seen wearing his regular ragged clothes.