I think I'v e shown my naiveté with that question. Though I'm familiar with the story, I am not familiar with that rendition, so I'm just catching up a little bit.
I find continuity errors in films interesting, and I had to do a little research on my own for this because it was tough to view the switching of the mask from one side of the character's face to the other as an error. I wanted to find out how it might have been used as an intentional storytelling device, or how it might have been a creative expression for a particular plot point.
During my initial search, I read something about a music video, which seemed separate from the 2004 film. So I thought maybe there was no need for continuity between two different presentations of parts of the story. Now, I've looked into it a little more and both scenes seem to be from the same movie.
I remember having a sense of ambiguity about the true nature of the phantom when I first experienced the Phantom of the Opera.
Is this in Christine's imagination?
Is the phantom an actual ghost?
Is there something about the opera house itself, and the phantom is a manifestation from a distorted reality caused by the place?
So, keeping in mind how the change in the mask's orientation could be an intentional representation for something in the story, rather than an error in making the movie, I read various synopses to jog my memory of the plot details, and was reminded that the scene in question occurs after the phantom entices Christine to a mirror where she sees his image.
Ah ha! Christine follows the phantom into his underground lair.
Or does she?
Either way, the scene is taking place as a mirror image.
So there you have it. The mask is on the same side of the phantom's face, but the viewer is seeing a reflection.
As an aside, there were other plot points I've been oblivious to until just now. Poor Raoul.
As for the mirror reflection, the Phantom is known to be a good magician as well as musician, and the film makers actually show Raoul find the mirror slid open, and try to go down the same path Christine had taken, but he is stopped by Madame Giry. Though I will note the arms holding torches which were on the wall when Christine and the Phantom walked to his layer, were not there when Raoul walked in. This shows the mask switch could have been imagined, however the whole story is based on a book which is based on a real event. If the book is based on an actual maniac who lived in the Paris Opera house and killed people, I'd imagine the Phantom would be real in the movie and play as well. The book created a plot by adding romance, however I don't think Gaston Leroux wrote it as a dream, I think he wrote it as a fictional base on a real event.