Playing Against Type: Michael Crawford was a well-established light comedy/musical actor in the U.K. when he originated the role of the Phantom in the original London staging. Even he was surprised at the casting. He has been quoted saying that when Andrew Lloyd Webber told him he wanted him for Phantom, he thought he meant for the part of Raoul.
At the end of the show, as Christine leaves the Phantom, he picks up her discarded wedding veil and cradles it as he weeps her name. This was never in the original script and was ad-libbed by Michael Crawford at some point in the show's original run.
Earlier in the show, when Christine faints at the end of "The Music of the Night", the Phantom kneels beside her and takes her hand as he sings the final lyrics. This too was not part of the original script and was improvised by a Phantom during a production in San Francisco. When word spread about how well this gesture was received by the audience, it quickly became part of the standard Phantom performance.
An inverted example: In the original London production, the Phantom catches Christine as she faints and carries her to the bed (see the Music Video that was made for "The Music of the Night"). This was initially done in the Broadway version, but when an actor injured his back during the stunt, the actors' union forbade it. Ever since then, London is the only venue where the Phantom carries Christine. In every other location, she faints and falls to the floor—from this minor detail alone (foreign languages aside) you can determine if a YouTube clip of this scene is of a London edition or elsewhere.
What Could Have Been: There were plans for a live-action film of the musical in 1990, to star Crawford and Brightman in their roles from the musical. The original script was being written before Brightman's divorce from Webber, and the project was left in Development Hell for some time before becoming the 2004 film.
"The Music Of The Night" ends on what many fans feel is an ambiguous note—the lights go out, raising the question of whether or not Christine and the Phantom had sex—or more accurately, given her unconscious/entranced state, he raped her. The original draft of the movie settles the question by actually having the Phantom get into bed with the unconscious Christine and for the scene to fade out as he drew the curtain around them, leaving little doubt as to his intentions. This was changed to as unclear as it is in the show—are her missing stockings a Continuity Error or something more?—as it would have been hard to continue presenting him as a romantic hero after such a blatant violation (or it would have been too obvious, even to the most naive viewer).
On the casting of the musical side of things, Steve Harley, an UK singer trying to make a comeback, was actually cast to star as the Phantom and went as far as recording the first single of the titular "Phantom of the Opera" song, but was sacked just before rehearsals began and replaced with Michael Crawford. Needless to say, the comeback never happened.
In the late 1990s, Antonio Banderas was being considered for the role of the Phantom in the film adaptation, perhaps alongside Kate Winslet as Christine.
Back in the late '80s, Michael Jackson thought he should play the Phantom in the movie!
Alan Jay Lerner, one of the most renowned librettists of all time and co-writer of shows like My Fair Lady, was going to write the words for Phantom but died when he had only just started.
Why is the Phantom's mask on the poster different from the one seen in the show? It's because that was the original mask design. However, it was soon realized that this 3/4 mask would make it REALLY hard for the Phantom to emote for the cheap seats, so the mask was cut in half.
Keira Knightley, Charlotte Church, Katie Holmes, and Fantine were considered for the role of Christine in the film—and Jean Valjean was a contender for the role of the Phantom.
On the movie side of things: Universal tried to make sequels to both of their adaptations of Phantom, but neither time did it work out:
In 1929, Universal announced plans for The Return of the Phantom, which would have featured sound and, astoundingly, full color throughout the whole movie! Plot details were never given, although Chaney wouldn't have returned (he had switched studios to MGM). In the end, Universal decided to go with the less expensive option of adding dialogue and new sound scenes to the original movie.
After the 1943 movie became a hit, they announced a sequel for 1944 called The Climax, which would've presumably resolved the minor Sequel Hook at the end of the original and feature the return of the Phantom. The Climax actually did come out in 1944 as promised, but all ties to Phantom were dropped, as Claude Rains was unavailable to return. It did use the same sets, though.
The 1925 film was originally much closer to the book, with scenes including Raoul's visit to Madam Valerius, the Perros graveyard scene, and Christine's kiss redeeming Erik, of which only still images remain. Unfortunately the director didn't like this ending (which was strongly supported by Chaney, who wanted to make the film as close to the book as possible), and neither did test audiences, so it was replaced with the mob scene.