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.
Alternative Character Interpretation: If Harry's theory about how Fred and George pranked Rita Skeeter is correct then the lovable tricksters could be seen as mind-raping someone with a false memory charm to destroy their career, thereby exposing them to the ire of very dangerous people. Harsher in Hindsight much?
Draco's internal thoughts make references to stories and plays which are obviously versions of Death Note, Gargoyles, and Thundercats, with the heroes portrayed as villains and vice versa.
Hermione: I'm getting tired of hearing people talk about the Boy-Who-Lived like you're - like you're some kind of god or something. Harry: Same here, I must say. It's sad how people keep underestimating me.
He's still a Villain Protagonist at worst. And there's a little "pantsification" when Harry points out to himself that Draco is not a psychopath — he's just the product of a very old and familiar culture in which nobles are above the law and in which you don't treat enemies as people. One of Harry's major goals after all is to "turn" Draco. And while that may be rationally excusable, Harry at several points implies he considers Draco a genuine friend, despite him never having renounced the whole child rape thing.
Lampshaded when Daphne Greengrass says Lord Malfoy would skin his son alive and turn him into trousers if he heard him talking against blood purism.
"Draco Malfoy smiled, metallic robes gleaming in the light of his full corporeal Patronus; it was a smile both arrogant and dangerous, like being turned into a pair of leather pants was beneath his concerns."
How about Chapter 17, in which Harry attempts to factor the product of two prime numbers using the Time Turner? (More generally, he comes up with a method to solve NP-complete problems, that is, problems where you can check a solution quickly, but finding that solution requires searching a gigantic solution space.)
Techically NP-complete problem can be solved quickly if P=NP.
Or Chapter 4, with its off-hand mention of how someone could make a lot of money by exploiting the difference in the relative prices of silver and gold in the Muggle and Wizarding economies. (Buy gold from wizards, sell it to Muggles, use the money to buy silver from Muggles, sell the silver to wizards, and end up with more money than you started with. Or, if the imbalance is in the other direction, buy silver from wizards and sell it to Muggles for gold.)
In chapter 26, Harry and Quirrell have a discussion in a scrying-proof location called Mary's room.
The "Slytherin System" described in chapter 63 is a version of onion routing, the anonymous networking technique used by Tor.
Growing the Beard: As the (edited) first chapter puts it: "This fic is widely considered to have really hit its stride starting at around Chapter 5. If you still don't like it after Chapter 10, give up."
McGonagall: What sort of contingency do you imagine this kit might prepare you for, young man?
Harry: One of my classmates gets bitten by a horrible monster, and as I scrabble frantically in my mokeskin pouch for something that could help her, she looks at me sadly and with her last breath says, 'Why weren't you prepared?' And then she dies, and I know as her eyes close that she won't ever forgive me -
As of chapter 89, it turns out that kit didn't help Harry as much as he'd been hoping. Mainly due to the timing of his arrival.
In Name Only: Most of the characters who differ from their canon selves do so by way of an Alternative Character Interpretation, but Harry and Quirrell are simply nothing at all like their canon counterparts. Being raised by an Oxford professor is a rather weak Hand Wave for Harry being a freaking Child Prodigy with a completely different personality. If you want to get any enjoyment out of the story, you pretty much just have to accept at the outset that Harry has been replaced by a different character for the sake of a "rationalist in the Potter Verse" plot. And canon Quirrell was decidedly not a Badass and, in fact, was basically just some sucker manipulated by Voldemort. Methods Quirrell did have some of the character's canon traits early on, but they're quickly dropped after becoming The Artifact.
Quirrell is the powerful, intelligent, and charismatic Tom Riddle and Harry is the memory-stripped horcrux, with all of the original's intelligence and a rather different upbringing.
Magnificent Bastard: Draco took lessons on how to be one, but so far he's only a beginner. The true Magnificent Bastard of this fanfic is, of course the one and only Professor Quirrell. Without spoiling anything:
Exhibit C: Bellatrix Black has been broken out of prison by him and Harry.
Marty Stu: We have a heroic Marty Stu and a a villainous Marty Stu. Whether they balance out or add together is up to the reader.
Memetic Mutation: Chapter 13: YOU HAVE LOST THE GAME (Probably unintentional, but who cares?)
Misaimed Fandom: The author, like a lot of readers, seems to have missed the point of Ron, and "sees no reason for him to exist". Canonically, Ron represents emotion, as Hermione represents reason. Largely excising him from the story leaves out some great opportunities for character development for the hyper-rational Harry. On the other hand, their friendship was founded largely on Harry not being kind of a jerk.
When Harry catches the Remembrall, and it glows like a sun.
McGonagall's speech about the dangers of transfiguration.
If you transfigure your hair blonde it will fall out. If you transform your skin to be clear... you will be very ill and spend a long time at St.Mungos.
The terrifying Welcome to the Real WorldOmake in Chapter 64.
After meeting the Dementors, Harry briefly becomes hyper-rationalist. Specifically, he divides everyone into useful or non-useful categories. If they aren't useful, if they're doing so much as annoying him by crying, he wants to kill them.
Ron the Death Eater: Subverted. While early on, Harry is very dismissive of Ron and it looks like he's going to be written out of the story, in chapter 31, he shows up again, as one of two chief strategists in Hermione's army. Unlike Harry, Hermione is better at recognizing the talents of others, and Ron is a master chess player.
Second Verse Curse: Harry only knows the first and last couple of lines of Tom Lehrer's "Be Prepared"; his parents rather wisely didn't teach him the rest.
Tastes Like Diabetes: Harry's "romantic" first date, organized by the rest of the girls in his class. He is not. Happy. At all.
Toy Ship: Harry and Hermione are eleven/twelve years old, even if they don't act like it. Everyone believes they will end up together - except the 'loving couple'.
Unfortunate Implications: Quite a few instances, most explained by the author as Harry not having all the facts at his disposal. Not all readers were entirely convinced. See the discussion page for debate on some of these.
The apparent take on the breakdown of Snape and Lily's friendship has drawn some flak, causing Yudkowsky to irritatedly point out that 'views expressed by Severus Snape are not necessarily those of the author'. He later admitted that he had been labouring under certain misconceptions regarding the nature of their relationship prior to the whole 'mudblood' incident.
And then there's this bit from Chapter 7, which was actually toned down from a previous version after that one engendered even more umbrage:
"And in the slowed time of this slowed country, here and now as in the darkness-before-dawn prior to the Age of Reason, the son of a sufficiently powerful noble would simply take for granted that he was above the law. At least when it came to a little rape here and there. There were places in Muggle-land where it was still the same way, countries where that sort of nobility still existed and still thought like that, or even grimmer lands where it wasn't just the nobility. It was like that in every place and time that didn't descend directly from the Enlightenment."
Some readers were offended by the seeming implication that this sort of thing never happened anymore in Western countries, and was automatic in non-Western ones, which they saw as privilege blindness. Again, see discussion page.
Also, the crack about Padma Patil, 'whose parents came from a non-English-speaking culture and thus had raised her with an actual work ethic'. Readers from English-speaking cultures disliked it for... obvious reasons, whilst readers from non-English-speaking cultures disliked it because it smelled somewhat of the patronisingly racist model minority stereotype.
Apparently, the only thing keeping Petunia with Vernon Dursley in-canon was that she didn't think she was pretty enough to get someone better. Never mind that the canon indicates that they sincerely love each other and Dudley, this Petunia has enough strength of character to leave Vernon after he wants to give their future child a silly name, but not enough to even try and convince him otherwise.