In Chapter 9, Sally-Anne Perks is sorted before Harry as in canon, and in reference to this fic she is described as "a pale waifish girl who looked oddly ethereal - like she might mysteriously disappear the moment you stopped looking at her, and never be seen again or even remembered." Sure enough, she makes no further appearances.
In Chapter 12, Quirrel channels Darth Vader, when he addresses the students of Hogwarts:
"Perhaps I can find new ways to motivate you."
In Chapter 13, one of the notes written to Harry by the Game Controller is a reference to The Hitchhiker's Guide to the Galaxy: "Ten out of ten for style, but minus several million for good thinking."
In Chapter 14, Harry says "And if someone bumps into me the Time-Turner will not break and will not trap the whole castle of Hogwarts in an endlessly repeating loop of Thursdays." in reference to this fanfic.
In Chapter 17, McGonagall discusses the recent disastrous employments of two Defense professors, Professor Blake (who was caught with THREE fifteen-year-olds in a broom closet) and Professor Summers (who failed to teach material correct in the Harry Potter universe).
And now — to Death Note, or should we say, Tragedy of Light. And to Gargoyles. Both of which are apparently children's stories in the Wizarding World, the latter of which is meant to teach young Slytherins about a cunning bussinessman (unnamed, but assumed to be Xanatos).
In Chapter 23, Harry makes an analogy involving an invisible dragon that is taken almost verbatim from The Demon-Haunted World.
According to Word of God, the line "And then Janet was a Squib" was not intended to be a reference to the last line of DOOM: Repercussions of Evil, but it's an amusing coincidence nevertheless.
Chapter 27: Mr. Bester is the Legilimens hired to train Harry. Harry creates an alternate persona in his mind to try to foil Bester's Legilimency; this persona is Kimball Kinnison of the Lensman series.
In Chapter 39, Dumbledore taps his fingers through a black plate inscribed with the word "Leliel", a reference to the 12th Angel from Neon Genesis Evangelion.
In Chapter 43 we learn that Harry plans to become an Animagus so he can turn into a peregrine falcon
In Chapter 46, Harry gives Hermione a letter that contains the answer to a mysterious question. The reference, you ask? The wax seal on the letter is inscribed with the number 42.
In Chapter 47, a reference to the founders of Hogwarts fighting Lord Foul.
Also in Chapter 47, Harry extinguishes his light with the word dulak; the typical word for extinguishing light is nox, Harry instead used the word the Raistlin Majere used to darken the Staff of Magius in the Dragonlance series.
Chapter 51 references Tom Lehrer, quoting the first two lines of his song "Be Prepared". It also includes Harry saying a password that contains the word "friend". And the world "melon", which sounds like the elvish word for "friend". And swordfish, as a reference to the Marx brothers (because The Password Is Always Swordfish). The Tom Lehrer reference is also a callback to Harry quoting the song to explain why needs to be Crazy-Prepared to McGonagall in chapter 6 (see also Second Verse Curse below).
"I am going to be in Ravenclaw. And if you really think that I'm planning to do something dangerous, then, with respect, you don't understand me at all. I don't like danger, it is scary. I am being prudent. I am being cautious. I am preparing for unforeseen contingencies. Like my parents used to sing to me: Be prepared! That's the Boy Scout's marching song! Be prepared! As through life you march along! Don't be nervous, don't be flustered, don't be scared — be prepared!" (Harry's parents had in fact only ever sung him those particular lines of that Tom Lehrer song, and Harry was blissfully unaware of the rest.)
Later edited to replace Miles with Lupe Cazaril. Word of God says that this is because Miles Vorkosigan is already attending Hogwarts.note And because apparently some people complained about Sci Fi references in a fantasy novel. Which makes one wonder if they even read the previous 69 chapters.
There is also a character called Mad Drongo in this chapter, although he goes by Adrian Turnipseed.
Quirrell is suspected to be a man called David Monroe, an inspiring figure throughout the last war. But he's not Less Wrong's OC; the character shares a name and reputation with one from nonjon's fic A Black Comedy. This David Monroe turns out to be a Tom Riddle created when the Diary horcrux ate Neville Longbottom; Quirrell/Monroe is Voldemort in disguise, after coming back from Albania. Perhaps the Diary was there in the Methods-verse? Both Monroes are at one point called 'the next Albus Dumbledore', too.
Harry: "Sir Gareth, owner of a transportation company that won the 19th-century invokedshipping wars... monopoly on oh-tee-threes... I see".