Factual error: Raoul is the Vicomte de Chagny and he gets called that throughout the movie, even during the auction (which shows he didn't change titles when his parents or his brother died, for example). Yet Christine's tombstone calls her a countess when it should have read viscountessor, even better, vicomtesse.
Factual error: The masquerade is set on New Year's Eve. We know that because its poster reads "Bal masqué de la Saint-Sylvestre" - St. Sylvester's Day is December 31st and it's common in French to call that day by its saint's name. Firmin (or André) says that it's been "Three months of relief, of delight, of Elysian peace." This means that the events on the opera house's roof took place in late September or early October at most. When Paris gets snow, it's usually in January, the coldest month according to Météo France. With average temperatures of 15 degrees in October, and higher in September, having a good centimetre or two of snow on the rooftop at that time of year is quite implausible.
Factual error: In the film, most of the characters don't wear nearly enough stage makeup. In "Think of Me", when Christine is performing in front of a packed auditorium, for example, she would have needed a lot of blush, eyeshadow, eyeliner, etc. just to look "normal" from the audience's perspective. Instead, as you can see by watching the film, she looks pale and washed out.