Continuity mistake: After leaving the book store, in an overhead shot Belle passes a shop just as a woman is pouring water towards the downspout, and in the next shot the shop suddenly has a large hanging pipe sign and a table under the window, the green shutters have vanished on the right window, the wood trim has changed, etc.
Super Grover
Continuity mistake: In the overhead wideshot right before Maurice walks in there's a green mat by the doorway, and nothing hanging over the large window, but when Maurice walks into the tavern there's a blunderbuss hanging over the large window, and the mat has vanished.
Super Grover Continuity mistake: After Maurice is thrown out of the tavern Gaston whispers his plan to LeFou, and when they begin to dance we see an angled wall with a dart board, bow and arrows, but the problem is that angled wall with the dart board, bow and arrows did not exist in the overhead shot, right before Maurice walked in.
Super Grover 
Continuity mistake: When Belle is reading her book before Gaston walks in to propose, the bellows hangs from a hook on the fireplace stones under the mantle, but when Gaston is talking to Belle the bellows now hangs directly from the wood mantle, though it's back to the original way when Gaston knocks over the rocking chair.
Super Grover Continuity mistake: During Gaston's song, when they sing "Give five hurrahs, give twelve hip-hips," LeFou's beer tankard switches from his left hand to his right hand, between shots. Additionally, one of the wall's wood beams near the fireplace has vanished behind LeFou, then reappears. The same thing happens again later, after they toss Maurice out the door.
Super Grover Continuity mistake: During scenes at the tavern, the shelves between the brew barrels keep changing between being quite ornate to being ordinary shelves.
Super Grover Continuity mistake: While Beast is bathing in the bathtub Lumière is standing on a stool with two level foot rest bars, but in the following shot the stool has only one level of foot rest bars, then it's back to two levels again.
Super Grover Continuity mistake: Right before Belle's father enters the tavern, watch the bar on the left: First there's just one man. The father enters and a bartender plus a guy next to him appears. Then Gaston asks "Who's got Belle locked up in a dungeon?", and all three disappear. Then the father says "A beast", and the bartender and first villager appear, but not the second man.
Sacha Continuity mistake: After the Gaston song ends there's a wide shot where there's a bare wall by the doors. When Belle's dad enters, a drinking horn hanging on the wall has appeared.
Sacha 
Continuity mistake: After being stabbed with the arrow, Beast falls over a balcony and then falls over on another rounded balcony, next to the edge. Then the angle changes and Beast is lying on the middle of a long rectangular structure.
Sacha Continuity mistake: After Cogsworth becomes human, Chip and Sultan walk in but suddenly Belle, Beast, Lumiere and Cogsworth disappear, only to reappear 5 meters ahead in the following angle.
Sacha Continuity mistake: While Belle is reading a woman in a house pours water on the drain pipe by an empty window. Belle avoids the water by pushing a wall sign and right then two vases with flowers appear.
Sacha Continuity mistake: After the baker cries "Marie, the baguettes!", there's a wide shot of the place and he has disappeared.
Sacha Continuity mistake: When Belle sings "Madame Gaston" there's a huge barrel against the wall, which disappears in the further shots.
Sacha Continuity mistake: After Gaston walks out of the puddle, a wide shot of Belle's house shows there are no cellar doors, but in the close-up they suddenly appear.
Sacha 
Continuity mistake: After Mrs. Potts sings "there might be something there that wasn't there before", angle changes to her telling Chip "I'll tell you when you're older" and his dent swaps sides.
Sacha Continuity mistake: Gaston throws the closed satchel with coins at the asylum guy, but when he reaches for it it's open.
Sacha Continuity mistake: When Gaston enters the palace he sees a mop. In the aerial angle it has a puddle of water around, which disappears in the close-up.
Sacha Continuity mistake: After Belle discovers the rose and Beast shows up, check a green book behind her. When the angle changes a red one has magically appeared.
Sacha Continuity mistake: The first time Belle discovers the rose it's facing a 12 o'clock position; when the Beast jumps in, the rose is facing a 3 o'clock position.
Sacha 
Answer: The servants in the castle are transformed into enchanted objects because of the spell, but there are still plenty of other objects in the castle which were not originally people.
wizard_of_gore