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.
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.
Continuity mistake: During scenes at the tavern, the shelves between the brew barrels keep changing between being quite ornate to being ordinary shelves.
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.
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.
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 Belle comes down to dinner she leaves her coat in her room. Later, after Belle runs out of the West Wing, she grabs her coat while running down the stairs.
Continuity mistake: When Belle goes to open the door for Gaston, her chair is close to the carpet on the floor. Then when the shot returns to this area, the chair is much further from the carpet.
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: When the Beast shows the mirror to Belle she is reflected in it, but for the rest of this scene she isn't.
Continuity mistake: When Gaston says "Now when Belle and I come out that door", you can tell that he has no instrument, only the musicians do. But in the next shot, Gaston has a tuba in his hands, and he slams it on top of Lefou's head.
Continuity mistake: When the Beast is shown falling into despair after scaring Belle away from the West Wing, the pieces of rock on the ground have all either changed position or appeared out of nowhere from the shot when Belle first saw the enchanted rose.
Continuity mistake: After Chip taps the spoon its position changes between shots.
Continuity mistake: When Cogsworth falls down the stairs while trying to stop Maurice from going into the room, a lot of his clockwork falls out and lands on the stairs. But in the next shot, it's all gone.
Continuity mistake: In the scene where the villagers try to imprison Maurice, there is a lot of snow on the stairhandle. When Belle comes out later crying "My father's not crazy", the snow is gone.
Continuity mistake: When Belle enters the West Wing, there are no candles next to the door. Later, Gaston enters with his bow, and now there are several candles next to the door.
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.
Continuity mistake: When the Beast is waiting for Belle to come to dinner, there is a fireplace with statues of lions on either sides and a pillow next to one of them. However, a few seconds later, the pillow is now in front of the statue.
Continuity mistake: In the scene where Maurice's Rube Goldberg-ish woodcutting invention works for the first time, we see the piece of wood fly over onto the stack. There is no window there or anything made of glass for that matter, yet in the next shot we hear glass breaking from the wood flying over there.
Continuity mistake: Belle's nails disappear and reappear throughout the movie.
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.