These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
The 2009 installment is in particular very divisive because of Moore's treatment of Harry Potter.
Complete Monster: Hawley Griffin, aka the Invisible Man, is a psychopath recruited by England so his powers could be utilized for special missions. Introduced hiding in an all-girls boarding school, Griffin's been taking advantage of his powers to rape the teenagers there. He's already impregnated three girls and is apprehended in the process of raping a fourth. When he joins the league, it's not out of any sense of altruism but because he's been promised a cure for his condition, a pardon for his crimes, and a large sum of money. During his tenure on the team, Griffin displays streaks of cruelty and cowardice in equal measure. At one point he beats an innocent constable to death simply because he wanted the man's clothes, and at the climax of the team's first adventure, Griffin attempts to abandon the league to their deaths when things get too dangerous. With the arrival of the invading Martians, Griffin eagerly approaches them and sells out his entire planet to the invaders just so he can rule alongside them. Griffin gives the Martians information on where the human artillery positions are so they can slaughter their opposition, tries to get his teammates killed by selling out their hideout's location, brutalizes Mina Murray while stealing valuable military information, and advises the Martians to use their Red Weed to destroy the Thames and incapacitate the Nautilus. In a series where even monsters can be heroes, Griffin was never anything but a selfish, megalomaniacal snake who was willing to let his race be butchered and enslaved just so he could rule over what was left.
Crack Pairing: Since the series deals with the relationships between various fictional characters, this happens quite a bit. Most visibly with Quartermain and Murray, but it happens with minor characters as well. Frankenstein's monster and his wife Olympia from Tales of Hoffman come to mind.
Creator's Pet: Orlando is regarded as some as this in the Century trilogy. Worth noting though the character is a Base Breaker who divides opinion.
Moore's Grand Finale for Century: 2009 involves an epic face-off between Harry Potter and Mary Poppins. Just a few months after he wrote that scene (and almost exactly a month after the comic hit the stands) a battle between Voldemort and a swarm of Mary Poppinses turned out to be part of the Opening Ceremony of the 2012 Olympic Games.
Among many other tidbits, Century: 2009 manages to tie James Bond and The Avengers together into one universe with the revelation that Judi Dench's M in the later Bond films is actually an aging Emma Peel. Though we never get to find out M's true identity in the films, Skyfall actually did turn out to include a brief moment where Kincade, Bond's old groundskeeper, addresses her as "Emma" (presumably because he misheard "M" as "Em").
Les Yay: Mina has no use for Orlando when he's a male.
Offscreen Moment of Awesome: We never get to see the full exploits of the Second League of the Extraordinary Gentlemen, and their very much indeed awesome sounding encounter with Les Hommes Mysterieux is only described in text on the Black Dossier. Also sideway referenced in text are the missions of Prospero's Men, The Third League of the Extraordinary Gentlemen, Der Zwielicht-helden and Les Hommes Mysterieux themselves.
We also see far too little of the League of the 1780s, featuring Lemuel Gulliver, the Scarlet Pimpernel and wife, the Scarecrow, Fanny Hill, and Natty Bumpo. Most of what we do see when they appear is when they've largely retired from adventuring and are touring the world indulging their more hedonistic tendencies.
Take That, Scrappy!: People who disliked Harry Potter or who liked it but felt it was overrated in esteem and especially found the title character less interesting than the supporting cast enjoyed Moore's takedown of it in Century Vol 3.
The announcement of the Century trilogy initially had fans buzzing because they thought they'd finally get to see the original graphic novel's premise applied to 20th century fiction. And they did...except, instead of creating a new team of champions for a new era of fiction, Moore just made the two remaining members of the original Five-Man Band immortal, and added one consistent new member (Orlando) who quickly devolved into a Creator's Pet. By 2009, Mina and Allan have mentally aged so much that they barely even resemble their literary counterparts (which kind of kills what made the series fascinating in the first place) leaving behind little more than ultra-obscure background references.
Calling truth back to fiction, the idea of a large literature cross over is going to play out very differently depending on who is doing the writing, Alan Moore himself should have no excuse but to expect a lot of people are going to totally respect his due diligence for research but find his story choices, to be a complete utter disaster. But in truth there's no real way plausible to please a majority here.
Unfortunate Implications: Usually parodied, but Black Dossier's Sexfiend Golliwog definitely qualifies. Though knowing Alan Moore he fully knows about these and is chortling to himself as people get in a huff about them. As the Values Dissonance shows he does like playing around with Un-PC notions.
Values Dissonance: The comic deliberately fakes this trope to create aesops such as "ORIENTALS, while BRILLIANT, are EVIL". Which we would like to stress is a verbatim quote.
What Do You Mean, It Wasn't Made on Drugs?: The Beatnik novella from the Black Dossier reads like this, which, given the source material, isn't surprising. If one takes the time to actually decipher the text, the plot seems to involve Fu Manchu and Professor Moriarty's descendants (Dean Moriarty and Doctor Sax, respectively) continuing a family feud by unleashing an ancient Aztec linguistic virus made from centipedes. Oh and the virus actually turns out to be Lovecraftian Eldritch Abominations.
Hilarious in Hindsight: The movie's Evil Plan involves a mysterious bad guy (who's eventually revealed to be Professor Moriarty) trying to start World War I a few decades early. Sherlock Holmes: A Game of Shadows, which came out almost a decade later, was about the same thing. In this film, Moriarty even references the Reichenbach falls as where "that man died." Perhaps he got some plastic surgery, and tried to start his Evil Plan all over again, but went more ambitious by using the League?
Richard Roxburgh would also go on to play Dracula in Van Helsing, which also featured a Mr. Hyde a year later.