Leroux's original novel and its fandom contain examples of:
Alternative Character Interpretation: In the case of the Phantom, it's done on purpose in the Broadway production. However, the original novel is much more straightforward about how we're supposed to interpret that character.
On the other hand there is a lot of this concerning Raoul and especially Christine. She has been interpreted as a child-like idiot savant, a young woman suffering from a severe Electra complex, and even a straight-out victim of sexual abuse.
Big Lipped Alligator Moment: In the original novel, a character known as the "brown man" is introduced, living in the sewers parallel to, and only intersecting momentarily, Erik. It's explained that he's a hermit monk, and that he's just always been there. Erik is understandably more frightened of HIM than he is of Erik. He is never mentioned again.
Interestingly, this character is a lot closer to the real figure Erik was loosely based on.
Macekre: The English translation by Alexander Teixeira de Mattos, which was the only one available until 1990. It's now in the public domain, so any English edition that does not specifically credit a translator by name is most likely de Mattos' Macekred version.
The famous musical and myriad other adaptations further contain examples of:
Actor Shipping: Ramin Karimloo and Sierra Boggess, who played respectively the Phantom and Christine in the original Love Never Dies and the 25th anniversary at Royal Albert Hall, get a lot of this from the phandom, due to their chemistry onstage and in real life, with the term "Rierra" designating them. There are frequent arguments about them dating or not... until one discovers Ramin is actually happily married with two kids. Though, when you come to think of the latter... you can actually wonder how Ramin's wife feels whenever you see Sierra and him in The Point of No Return...
Alternative Character Interpretation: And how! Erik has become more or less the poster-child for woobiedom. Try to find a fic where he ends up miserable and alone. The fan base is quite split over this, but a strong majority finds Erik to be by far the most sympathetic character in the book/play/film. And how you feel about this will make a difference on what you think of Love Never Dies. Fan works aside, there's been a lot of different interpretations of who Erik actually is—he's been portrayed as everything from a doomed romantic who just got pushed a little too far (Kopit/Yeston version) to a slasher-style killer who sold his soul to the devil and flays the skin from his victims (the 1989 film starring Robert Englund, yes, Robert Englund).
Christine. Is she genuinely in love with Raoul, or is she unconsciously attracted to him simply because he can save her from her Stalker with a Crush? Notice on the rooftop scene, after Raoul declares his love for her, Christine immediately says, 'Order your fine horses, be with them at the door...'
When she kisses The Phantom at the end, is it because she really loves and/or pities him or because she's trying to save Raoul?
It's interesting to note in the stage production that while both Raoul and The Phantom explicitly say they love Christine and make that declaration to her, she never says it back to either of them, not even in song.
Awesome Music: The Overture/title theme, "Music of the Night," "Masquerade," and the final scene, among others. Really, the whole score can qualify.
Ear Worm: DAAAAAAAAAAAAAAAAAAAAA, DA DA DA DA DAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA, DA DA DA DA DAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA!
The "Wandering Child" trio. Good thing it's gorgeous.
"Masquerade", in all of its iterations.
"The PHAAAAAAAAAAAAAAANTOM OF THE OPERA IS HERE...INSIDE YOUR MIND!" Damn right it is.
It could be said that nearly every song is an Ear Worm
Oh, Lord, it's been 26 years since I first heard "Music of the Night" and the damn thing still won't go away.
"Poor fool, he makes me laugh! HAHA-HAHA-HA!"
Fan Hater: Plenty, who believe the show is nothing but style (and gooey romance) over substance. Interestingly, though, liking the book too is a good way to find redemption with the hatedom... so long as you say the book is better.
Fanon Discontinuity: A lot of fans would like to forget The Phantom of Manhattan, a novel by Frederick Forsyth that was based on the original plans for a sequel to the musical in the late 1990s, ever happened. Love Never Dies appears to be heading in the same direction.
Harsher in Hindsight: The fact that Andrew Lloyd Webber essentially wrote the musical for his wife and muse, Sarah Brightman, in order to make her a star - he even gave her a chance to show off her skills en-pointe by switching Christine from a member of the chorus to one of the corps de ballet - becomes all the more awkward and depressing after their divorce.
Especially so upon watching the guest performance at the end of the Royal Albert Hall performance. She was actively inching away from him and grabbing Michael Crawford's hand. (ALW managed to hold her other hand, though.) Although Sarah's still smiling and laughing, she looks like she wants to get as far from ALW as humanly possible.
Some Phantom fans (or "phans") say that the makeup on Phantom is a cop-out, as it's still only over one half of his face, but, let's be honest - a man who's good-looking on one side and like a rotting steak with an eye on the other alongside a partially exposed cranium and about as much hair as the average healthy person cleans out of their brush at the end of the month is still deformed enough to be believably outcast from Victorian society, even if he's not the "living corpse" Leroux described. (And with those conditions, being handsome on the other side tends to only make the deformity look worse.) Word of God says that:
the half-mask was created because it was very difficult for Michael Crawford to sing properly through a full-face mask,
Both Crawford and Andrew Lloyd Webber have said that it just took too long to apply make-up all over his face; Lloyd Webber was apparently worried no actor would play the role for very long if it required five-plus hours in make-up. Even with a half-mask, it takes time: by the end of Crawford's tenure, the make-up application was down to two hours, and that's about how long it takes for his successors.
And, in addition to all that, it's very hard for an actor to emote to people at the back of the theatre when most of his face is covered half the time.
And in the Takarazuka Revue productions of the Arthur Kopit/Maury Yeston musical, both Wao Youka and Haruno Surime◊ were WAY too pretty for their own good. Bizarrely, they both managed to make it work regardless.
Internet Backdraft: The following topics will cause your Phantom message board to explode: Michael Crawford, Gerard Butler, or Ramin Karimloo (especially vs. each other), Sarah Brightman, Emmy Rossum or Sierra Boggess (ditto), the movie in general, or Love Never Dies.
Irony: The fact the book has inspired one of the most famous silent film of all time AND one of the most famous musicals of all time. (Music was played by orchestras in the theater as a silent film played, but film musicals didn't come until sound was actually added to the film.)
Memetic Mutation: The conceit that only half of the Phantom's face is deformed, originally designed because the full mask was interfering with Michael Crawford's singing, has become the iconic visual for not only the Phantom himself but any similarly deformed character.
Narm: The "Point of No Return" scene where Phantom sings a song of seduction, while dressed head to toe in a cloak.
Nightmare Fuel: While the unmasking scene in the 1925 film is considered Narm these days, it was absolutely terrifying to audiences at the time.
Here's a challenge: show the movie to a group of people who are only acquainted with the 2004 movie and/or musical and know nothing of the 1925 film. Chances are high there will be screaming.
While there are charges of Lighter and Softer leveled at the Lloyd Webber musical, there are several sections that are extremely dark and frightening, such as:
The Phantom laughing wildly as he makes Carlotta croak. He already sounds completely insane - "Behold! She is singing to bring down the chandelier!!!" - and takes malicious, gleeful delight in humiliating the poor woman.
The ballet scene that immediately follows this, as he casts ominous shadows on the backdrop, the dancers get more and more frightened and agitated, and the music more sinister. If you haven't seen the show before, you're just waiting for something horrible to happen; if you have seen it before, you're waiting for Buquet to drop.
Replacement Scrappy: Inverted. Raoul is widely hated in the fandom, but the number of people who hate him drops dramatically when the role is played by Hadley Fraser. "I hate Raoul, but I love Hadley too much to care!" is a common refrain, as is "Hadley is the only Raoul I've ever liked!"
Ron the Death Eater: Expect Raoul to get hit with this a lot by Erik/Christine shippers who make Raoul to be a horrible person to Christine (before Love Never Dies technically made it canon) despite the fact that Erik himself definitely has his own problems as well.
What an Idiot: It still wasn't exactly smart of Christine to unmask Erik in the novel, but at least there she had the excuse that it was a full face mask. She thought he was trying to hide his identity from her and - quite rightly, all things considered - wanted to know who he was, justifiably assuming there was a perfectly normal face under there. Christine in the musical, on the other hand, whips off the mask of a man who keeps only half his face covered - and therefore is probably concealing it for a very good reason. Such as to hide a deformity, perhaps? And she's shocked that he starts screaming at her? (Though the 'little lying Delilah' and general rough handling was too much.)
The current touring version switches the Idiot Ball from Christine to Erik. He removes his mask to bathe his face after loudly playing the organ, assuming that Christine will still remain asleep for a while longer. She walks up behind him, taps him on the shoulder, and gets a full view of his maskless face.
And in the miniseries too. Erik repeatedly warns her that his face is too horrifying to look at. She assures him that she loves him too much to be repulsed. He finally relents and takes his mask off. . .and it's so terrifying (though the audience never sees it) that she faints.
The Woobie: Erik gets this treatment in some versions, while in others he causes at least as much grief as he gets.
WTH, Casting Agency?: In addition to Crawford's celebrated Playing Against Type turn, the title character in the musical has been played by Paul Stanley (of KISS fame) and Robert Guillaume (until recently, the only black actor to play the Phantom. In all fairness, the casting department might be trying to avoid the Black Vikings trope, as well as the Unfortunate Implications of a black man lusting after and stalking a young white woman).
The 25th anniversary concert got a bit of this from the fanbase, as well — some were skeptical since the Phantom and Christine would be played by the stars of Love Never Dies (though, to be fair, they had previously played those roles in the original show as well); and since Raoul, Piangi, and Meg were played by actors who had no prior connection with Phantom while several popular alumni of the show were cast in minor background and chorus roles. Once the event actually took place, though, the casting was generally pretty well-received.
To a lesser extent, the musical itself.
At long last, after 26 years, Broadway cast its first African-American Phantom (Guillame's turn was as part of the national touring company), Norm Lewis, who debuted in May 2014. Thus far, opinion seems to be that his acting and singing talents are transcending the problematic above-mentioned tropes, as they did during his turn as Javert in the 2006 Broadway revival and 25th Anniversary Concert of Les MisÚrables.