Factual error: The film is set in 1997. There is a scene where Amelie knocks on a house door and in the background is a new model VW Beetle. These weren't available until early 1998. You can also see several scenes with various new models of Fiat Punto and VW Golf which weren't available until 1999.
Continuity mistake: When Nino goes to 'Les deux Moulins' for the first time, we can see Amelie writing the menu on a glass right behind him. A few shots later, we see the glass again and the handwriting is quite different. That's easy to see if you look carefully at the 'd'. Later on, we see the glass once more, and the handwriting has changed again.
Question: How does Raymond Dufayel aka Glass Man know Amélie is looking for Bretodeau/Bredoteau aka The Box Man. He says "I've lived here for five years. This is the first time we've met." Then adding that he never goes out on the landing, they're all creeps. So my question is who told him Amélie was looking for The Box Man? Lucien the grocer boy maybe? As he delivers to his flat. Or maybe Madeleine Wallace the Concierge