Gaston's chair disappears from in front of the fireplace in the penultimate shot of the "Gaston" reprise.
When LeFou is chasing Footstool, he is missing his left shoe, which is in the dog's mouth, but when LeFou and his buddies burst through the door, his shoe is on. When the Stove scares them away by flaring up, his shoe is missing again. In the final shot of the mob fleeing, LeFou has his left shoe on again.
After Gaston shoots the bird, LeFou puts it in his hunting bag, but his bag disappears as he goes to pick up the larger carcass.
The Beast makes a huge mess of oatmeal and milk on the table while he is sloppily eating it. Later, when the Beast and Belle raise their bowls to each other, the mess has disappeared.
The Beast spills some oatmeal on his sleeves while he sloppily eats it. In the next shot of him, the spilled oatmeal has disappeared, and his sleeves are completely clean. When he attempts to eat his oatmeal neatly, the oatmeal spilled previously is back on him.
Gaston says that the book has no pictures, but earlier it's seen that it does.
In the opening scene of Belle's house the gear connected to the windmill gear is spinning in the wrong direction.
At 51:13 an establishing shot of Maurice's house shows the weather vane with cardinal directions in the wrong order: NWES instead of the correct NSEW order. Other shots of the house show the correct order.
Maurice is captured for trespassing in the Beast's castle. Belle also trespasses to find her father. The Beast could have just kept her without releasing her father, thus there would be no threat from the villagers or Gaston. However, a very similar scenario occurred at Auschwitz with a Polish priest named Maximilian Kolbe, who offered to take the place of a man about to be sent to the gas chambers. Merely stepping out of the line-up in the way Kolbe did would've been enough for him to have been sent to the gas chambers anyway, but the Nazis still accepted his offer and let the other man go, and the Beast essentially does the same with Belle.
When the Beast is sloppily eating his oatmeal, his eyes are white with blue pupils. In the next shot of the Beast, when he is seen grabbing the spoon that Chip nudged to him, his eyes are blue with black pupils.
During the song "Belle", Belle opens the lower door to the bookstore, and when she exits the building, the door is closed, despite her not closing the door.
It's difficult to see, but in the first shot of Gaston falling to his death, Belle, while holding onto the Beast, has her hair in a ponytail and her hair ribbon on, even though she didn't have it on and her hair was down.
In the first shot of Gaston falling to his death, Belle, while holding onto the Beast, has her hair in a ponytail and her hair ribbon on, even though she didn't have it on, and her hair was down once she came onto the balcony.
During the fighting scene between Gaston and Beast, Gaston says "Belle is mine!" But his mouth is saying something else. This is because, he was originally supposed to say, "Time to die!" but the writer changed it to fit Belle back in the scene.
Before Gaston attempts to propose to Belle, he kicks off his boots. But while he is walking around the house, distinct footsteps and jingles are heard, implying he has boots on.
Following Belle's title song reprise on the hilltop and just after Phillipe interrupts her moment, she says "Phillipe!" though her lip movements suggest that other dialogue was intended.
During 'Gaston' the bald man playing chess with Gaston is clearly seen placing a white squared bishop onto a red one. In chess, the two bishops on each side can only move or land on a square of the same color, so the man playing against Gaston actually made an illegal pass.