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.
Character mistake: At the beginning of the movie, during "Provincial Life", we see a fat lady trying on a hat in a hat store. The sign over the window, in French, reads "Chapeau" (hat). The correct way to identify that store would have been "Chapeaux" (hats) or "Chapelier" (hatter).






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.