Deliberate mistake: As Christine approaches the Phantom in his lair (just after he has abducted her), we see that she is wearing very dark black eye-shadow. Back in the dressing room after coming off stage, as she talks to Raoul, we saw her face in close up and she was not wearing any eye-shadow at all, even though the Phantom leads her through the mirror just after she has managed to slip on a robe over her undergarments and she has not yet changed to go out to supper (Raoul says she is to be ready in 2 minutes). Her hair becomes 'bigger' and wilder, too. The change in her appearance is a reference to her descending (voluntarily, I might add - he didn't drag her through that mirror) into the Phantom's dark existence and to her sexual awakening.
Deliberate mistake: On the rooftop scene after Raoul and Christine have left the Phantom, he bends down to pick up a rose, then runs to the statue and climbs up, and finishes his song. There are footprints in the snow all the way to the base of the statue. The footprints are a definite error, as they are next to each other instead of spaced apart which would have occurred if a person was running. And the footprints were not made by Christine and Raoul, they are in the wrong place for where they were standing.
Deliberate mistake: When Christine is in her dressing room right after Hannibal, all of the candles are shown going out. The Phantom and Christine begin to sing. There are no windows in the room and the candles have all gone out, yet the room is still somehow lit. The light is not coming from the mirror where the phantom is yet.