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.
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.
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: 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.
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.
Continuity mistake: After the baker cries "Marie, the baguettes!", there's a wide shot of the place and he has disappeared.
Continuity mistake: When Belle sings "Madame Gaston" there's a huge barrel against the wall, which disappears in the further shots.
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.
Continuity mistake: Gaston throws the closed satchel with coins at the asylum guy, but when he reaches for it it's open.
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.
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.
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.
Continuity mistake: When the villagers open the door with the tree trunk, they make a hole in the door, which disappears in further shots.
Continuity mistake: When Gaston shoots Beast, the broken part of the window swaps from separated and totally broken, to slightly broken between shots.
Continuity mistake: Right before "Be Our Guest", Lumiere kisses Belle's hand. In the first close shot, his arm flame is lit. The far shot then shows it out. Then the second close shot shows it lit again.
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.