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.
YMMV: The Fault in Our Stars
Alternative Character Interpretation: Some readers dislike Augustus for his grandiose mannerisms and his love of metaphor, but others argue that he was meant to be written that way, because wanting to be impressive and memorable is an established character trait of his.
Harsher in Hindsight: In-Universe, Van Houten insults Augustus' intelligence by saying his cancer must have spread to his brain. A Kick the Dog moment on it's own, but then Gus later reveals that his cancer did in fact return and has spread to the rest of his body.
Hatedom: A small but vocal one popped up after some clips of the movie were released, mostly accusing the story and its author of being pretentious and pseudo-intellectual.
Some Jewish Tumblr users dislike the use of the Anne Frank House in the story (particularly Augustus and Hazel kissing in the Secret Annex, and also Green remarking on how Augustus feels a kinship to Anne because she died of illness, which is a rather...interesting interpretation of Anne's death of typhus). It's worth pointing out, however, that the owners of the Anne Frank house liked the scene and allowed it to be filmed at the actual house.
With the release of the movie coinciding with the unfortunate underperformance of Edge of Tomorrow, some sci-fi fans have become rather vocally hostile to the movie, declaring it "romantic garbage". (It calmed down a little after Edge of Tomorrow made more money than TFIOS from overseas success.)
The book itself has basically developed a huge Broken Base on the internet in general. It's either a heartbreaking, beautiful story with incredible and important messages and characters or a predictable, pseudo-philosophical romance that falls into all the familiar traps of "cancer books" that it tried so hard to avoid.
Ho Yay: Isaac points out Augustus’s “physical attractiveness” multiple times. Also, Augustus claims that his hot body caused Isaac’s blindness. And on the dubiously canonical Q&A blog that John Green runs (see main page for link), Isaac is referred to as both “gay” and “a [future] ballerina.” Both are said in jest, but still.
Isaac accidentally grabs Augustus’ thigh. The first thing Augustus says to him is, “I’m taken.”
Hype Backlash: After the clip for the “it’s a metaphor” scene was shown at the MTV Movie Awards, it received a surprising level of backlash, due to people seeing it as pretentious when said out loud by an actor.
Plus, what he's describing isn't a metaphor, making him sound like a hipster who's just using random words he heard somewhere to sound smart (which, according to Word of God, is very intentional - Gus is a smart kid, but he uses a lot of words and concepts wrong, like any other teenager).
Jerkass Woobie: Van Houten. Yes, he’s a drunk asshat, but you have to admit he is sort of a tragic character.
Memetic Mutation: This book (not to mention the author) has a pretty big following on Tumblr, mainly for being a massive Tear Jerker and a major source of feels. A common Running Gag is for newtime readers to document their first readthrough of the book and the progressive regression into a blubbering puddle of tears.
“My x are y that I cannot fathom into z.”
“I the way you : slowly, then all at once.”
“It’s a metaphor; you put the x in between the y, but don’t give it the power to z.”
John Green: I just want to point out one thing here: When was the last time the girl kissed the boy in a teen romance? Ever? Has it happened ever? I seriously think it might not have happened ever.note This comment was met with immediate backlash, with people pointing out that this trope is much Older Than They Think. John swiftly corrected himself afterwards, admitting that he got a little carried away with his euphoria over the film being released.
The comment spawned a meme (largely from the book's critics) about John being the inventor of feminism.