Accidental Aesop: As Roger Ebert sarcastically put it in his review of The Movie, "I never knew reading was so dangerous. No child seeing Inkheart will ever want to be read to again, especially if that child loves its mother, as so many do." Ironic considering the overall intended message of the books.
Anvilicious: The power of the written word and the magic found in books.
Badass Decay: In a meta sense. In the book, Capricorn is seriously creepy and you can imagine that he'd be terrifying if you actually met him. In the movie, he's still evil, but he's also somewhat of a goof ball who apparently loves duct tape.
Base Breaker: Some fans weren't too happy with Inkdeath, which had Farid derailed as Meggie's love interest and be replaced by a new character who sweeps Meggie off her feet with his charm.
Crack Ship: Strangely enough, Basta/Meggie has gotten some attention. Some don't pay attention to the Foe YaySquick of an older man being with a girl young enough to be his daughter or the fact that he's threatened her and her father.
Darkness-Induced Audience Apathy: According to Fenoglio, he let both Capricorn and Basta survive his book while letting Dustfinger die, as he is rather pessimistic about the world, believing that murderers get off scot-free while the innocent die. This may have been the reason why he chose to write a sequel to rectify that.
Die for Our Ship: Let's just say that people weren't too happy about Meggie getting together with Doria instead of Farid.
Draco in Leather Pants: In the books, Basta is a sadistic murderer and arsonist who once sliced up Dustfinger's face (and much more recently murdered one of his oldest friends), and has threatened to do similar things to every single protagonist he's come across. In fanfiction, Basta is commonly portrayed as a somewhat misunderstood, but still a sweet and good-at-heart guy. GAH.
Part of this did come from the first book's implications that he was a more complex character than the other Fire Starters - Dustfinger even notes that Basta never enjoyed killing animals and hurting people like the rest of the group - but given that this is either dropped after Book One or implied (by the narrative) to not excuse his evilness, it's quite Egregious that people still insist as much. Especially given how they brush his indisputably evil deeds under a rug.
Fanon Discontinuity: Inkdeath? What is this Inkdeath you speak of? I know of no such horrible thing.
Some argue Inkspell was infinitely worse, although some people thought Inkspell to be better than Inkheart.
And then there's those who think each book was weaker. Or stronger. Or... you get the idea.
Fan-Preferred Couple: Some people were on board for the Meggie/Farid ship even after Inkdeath where Meggie gets together with a different character.
Despite both of them being Happily Married to their spouses, especially when they were in different universes, Dustfinger/Resa is pretty popular.
Fridge Logic: It's been demonstrated that people in stories can write their own stories, which you can in turn read into and out of. People in those stories can do the same thing, ad infinitum. This means that it's not only possible, but virtually certain, that our world is not at the top of the stack: that we are just the results of a story written somewhere else, and that that somewhere else is just another story, and so on.
Magnificent Bastard: Orpheus. Not above harassing and (implied) molesting a young woman half his age just for being pretty and the daughter of his biggest hero. "Stealing" words of the creator of the world he lives in to create strange animals and entertainment devices just for his own purposes. Oh, and he tries to get rid of any other person with the Magic Voice. Even if it's a 13-year-old girl. Doesn't stop at manipulating a pregnant woman and murder. Lovely indeed.
Narm: The books are this to the degree that they are unbearable at times.
Squick: The Meggie/Dustfinger pairing. Meggie is young enough to be Dustfinger's daughter, but this is strangely popular.
Tastes Like Diabetes: The film's ending is so ridiculously happy it's almost unbearable. Meggie defeats Capricorn and his men on her own, reads almost every character back into their own books, and somehow gets her mother's voice to return. To add onto the sugary ending, Dustfinger is read back into his book and happily reunites with his wife and it's implied that Meggie and Farid get together.