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.
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.
Complete Monster: Capricorn, which is thankfully made extremely clear in the novels, who burns entire houses to the ground and creates a horrific monster to murder his enemies. Also present is the Silver Prince, who forces children to work in his mines, murders the Laughing Prince's son, and bathes in the blood of faeries.
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 narative) 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.
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-yearsold 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.