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 viscountess - or, even better, vicomtesse.
Factual error: In the shot where Raoul and Christine are standing at the window of the Swarovski shop, the window shows the current Swarovski logo of a swan. In the time the movie is set, they still used the Eidelweiss as their symbol; it was not changed until the late 1980's.
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.
Suggested correction: When you watch "love never dies" he leaves her because the phantom won the bet, it's implied they got a "divorce" so she is still a countess.
But, in love never dies, it shows Christine dying in the year 1910, (when the whole thing was set) but on her tombstone, it shows that she died in 1913. Since Gustave is ten years old, this would make Christine in her late forties-early fifties when she had him, which is practically impossible. This is why I love LND's music, but the story is just too cheesy and inconsistent to the original for me. Since the original creator of the musical, Andrew Lloyd Webber, has chosen to call it a "stand-alone piece." and not a sequel, I would not use it as a reference for future endeavors with the trio.
Vicomtesse and Comtesse are two completely different titles. For Christine to become a Comtesse, Raoul would have had to become a Comte, but he didn't. He remained a Vicomte, therefore, Christine's tombstone should have read Vicomtesse de Chagny. It doesn't, so this mistake is valid.