Continuity mistake: When the Beast brings Belle into the library, there is a huge globe on the ground, but in the next shot, as Belle passes over it, the globe is much smaller and is now on the table.
Continuity mistake: In an overhead shot as the villagers enter the castle, there is a blond man in a brown coat carrying a torch. A second later, as the brawl begins, this man's torch has been replaced by an axe.
Continuity mistake: When Belle enters the bookshop, she pushes the lower part of the door open. When she leaves it is closed and she opens it again. (00:04:25)
Continuity mistake: In the very short scene where the Beast throws Maurice into the machine and it carries him away, the front entrance of the castle is utterly different from normal. For instance, normally there are no stairs leading up to the castle, the statues on either sides of the doors are different, the walls next to the entrance are shaped differently, and so on.
Continuity mistake: In the scene where Lumiere and Cogsworth are persuading Belle not to go to the West Wing, the width of the red carpet on the stairs changes, it becomes much wider between shots.
Continuity mistake: When the Beast brings Belle into the library the books on the table change between shots.
Continuity mistake: When Belle returns the book to the librarian, he puts it on a shelf, and it is leaning against other books. A little later, it straightens itself without the man touching it.
Continuity mistake: When Belle goes to the West Wing, from an inside shot, after she opens the door, there is a handle on both of the doors. It then cuts to a different angle and pans backwards, and now there is only a handle on the left door. (00:42:55)
Continuity mistake: There is a scene with Belle and Beast dining. Beast wolfs down his meal out of the dish and his face is covered with food. Belle looks shocked, so Beast then tries to use a spoon and he is completely clean. Belle smiles sympathetically and Beast is covered with food in the next shot. When they are both eating directly from the bowl, Beast is clean again. It is the same meal. The food is missing from his face, although not an uncommon thing for animators (especially of kids films) to do on purpose, Disney probably wouldn't consider it a mistake, but rather, a convention, to make the characters always look their best. (00:51:30)
Continuity mistake: When Belle arrives at the Beast's castle, her cape hood is down, hanging off of her head. In the very next closeup it's up on her head. (00:20:40)
Continuity mistake: When Cogsworth gives the tour to Belle, he is walking a very far distance from Belle. Yet in a closeup, he is walking much closer to Belle.
Continuity mistake: Just before Gaston proposes to Belle, the band members at his wedding change between shots.
Continuity mistake: Early in the film, we see the enchanted rose, and then the camera zooms away from the Beast's room and the castle. We see that there are several aspects of the castle that change during the Beast's fight with Gaston. For instance, in this shot we see that there is no window and the room opens directly to the balcony. This changes later. Second, the space along the roof is not as wide as it later is, and definitely not wide enough to have a fight. Third, we see strange statues of creatures that later appear in the fight- but no long row of these creatures such as appears later.
Other mistake: There are two gears on the top of Belle's roof, but both of them are spinning counter-clockwise. (00:02:45)
Continuity mistake: In the stained glass introduction, the rose in the beggar woman's hand keeps changing. Sometimes she is clutching it at the top, sometimes at the bottom, sometimes pinching it with her fingers.
Continuity mistake: When Belle meets Mrs Potts for the first time, Belle approaches the door to let her in. In the shot of Belle walking toward the door, the door handles are both the vertical "thumb-button" latch that you would grip the handle and push down on the thumb piece (with your thumb, of course) to release the latch. But in the next shot when she opens the door (and when she is first shown her room), the door handles are diagonal "lever style" handles that you have to turn downward with your whole hand to open the door. (00:30:10)
Continuity mistake: When we first meet the three blonde triplets, the one in the green dress has the Ariel-like bangs, but in the beginning of the Gaston song she has swapped hairstyles with her sister in the orange dress. When Gaston starts singing about eating eggs they switch back, but during the last shot of the song they're both sporting the red sister's hair.
Continuity mistake: When Mrs. Potts is singing during the song "Be Our Guest", the spot doesn't actually appear on her until she notices it.
Continuity mistake: When the household items fight the mob, six beermugs fling tomatoes at a man. It cuts and there are suddenly just five beermugs. (01:12:15)
Continuity mistake: Between shots of Gaston throwing the bag of gold on the table and the man taking a coin out, the bag opens by itself.
Answer: In the prologue, it states that the Beast must find true love by his 21st birthday, and that he had been cursed for ten years, so since his relationship with Belle takes place as the deadline approaches, he must have been 10 when he was cursed.