Other mistake: During the gypsy fair, when the young Phantom is hurriedly pulling the bag back over his head, you can see the actor's face from the side, through the bars of the cage. There is no deformity, even though the angle of the shot shows the top right of his face, where the mask is always worn later. Even moreso: his deformity is bumpy, and the side of his face is all baby smooth.
Other mistake: When the opera cast is rehearsing "Hannibal," Carlotta is asked to sing "Think of Me" for the new owners. She begins singing the song in the musical key of F Major, but is then interrupted by the falling oleo. A while later, when Christine is singing this same song for the owners (to fill in for Carlotta), she begins singing the song in the key of D Major (which is 2 whole musical keys lower). Assuming that's the result of the Phantom's tuition (there's no other plausible explanation for the change), the orchestra conductor of the opera couldn't know that Christine needed to sing the song in a lower key. This is also the case since it seems that everyone nearby is very surprised by Christine's beautiful singing, because they had never heard her sing a solo before.
Other mistake: At the end of the movie we can see Christine's grave. The inscription on her tombstone is in English and she is even called "Countess de Chagny" instead of "Comtesse." But the entire story takes place in France, and all the other signs and posters besides this grave are in French. There is no reason whatsoever why the inscription should be in English instead of in French, especially considering that the closeness between the words countess and comtesse would make the title easily recognisable even by non-French speakers.
Other mistake: While running to the rooftop, Christine always leads Raoul. She is the first to get up the stairs, and there's no room for him to pass her without her stopping her frantic pace (which she shows no sign of doing), yet somehow ends up only rushing out the door after Raoul does.
Other mistake: During "Don Juan Triumphant" Christine and Meg have MUCH less make up on than any other members of the cast, which is I suppose used to separate them and make them more noticeable, but on a stage that big it would be required to have a lot of makeup just like everyone else, because otherwise the audience can't see your face.
Other mistake: When the phantom sings behind Christine's mirror in her dressing room, she starts to walk towards it, entranced. It's obvious he is behind the mirror, and it's a one-way mirror. But, when she touches his hand, wouldn't the mirror have to be opened up? They act like she can just walk into the mirror.