No matter what universal laws Harry discovers, he will only be correct if he determines that the fundamental rule is that whatever Yudkowsky decides must happen then happens.
The Patronus can be used to send messages to anyone instantaneously, even in places where teleportation is limited. Chapter 53 spoilers: For example, Hogwarts and Azkaban. Why can't Harry send his Patronus to Azkaban while he stays at Hogwarts? Even if it's not possible, why has no one ever even asked about it? Chapter 85 spoilers: Especially after Harry becomes even more obsessed with destroying Azkaban and the Dementors.
Minerva's presence did make a final difference to how the prophecy turned out. If it had been just Severus there with Trelawney, obviously he would have figured out that it was meant for him, and that would have required it to be even more ambiguous and subtle to make him still go to the Dark Lord with it before working out what it meant.
Quirrell seems to be taking his teaching duties seriously, marking boring homework assignments and advising Hermione to leave Hogwarts for her own safety (though there might be other motives for that). This seems at odds with his cynical, unconcerned attitude, until you realise there was a time in canon that Voldemort wanted to be a Defence Professor.
Moody thinks rather than using a trapped Triwizard Trophy to teleport a victim (with a completely pointless return charm on it), an intelligent dark wizard would have someone simply toss the target a trapped Knut on their next visit to town. Quirrel used this exact method to take Harry to Diagon Alley (albeit consensually) earlier in the story, making this a call back (and reminder of Methods!Quirrel's genre-saviness compared to canon Voldemort).
In Chapter 74, the students who encourage Pansy Parkinson to think her soul has been eaten are all members of the Chaos Legion.
Quirrel's answer to Dumbledore after Harry killed a dementor makes us wonder why nobody caused him any problems after a Sarcastic Confession of this sort. Until we realize that the only people who would take this answer at its face value are those who know the answer to the "What lies at the center of a Dementor?" riddle, and those who had weren't likely to find Quirrel's goal in life to be all that bad.
On the same note, what everyone except Harry hears the Dementor say to Professor Quirrell is that "it knew [him], and that it would hunt [him] down someday, wherever [he] tried to hide." Harry assumes this is just something they've all constructed, rather than something the Dementor has actually said; whether or not this is true, the reader knows there's more meaning to that threat than the characters assume.
In Chapter 89, all the chracters who try to stop Harry are from the Chaos Legion, and those who help him are from the Sunshine Regiment
Daphne's lightsaber is a Blade of Greengrass
Dumbledore's "there would be nothing left of the world but fire!" in chapter 61 is what Severus is thinking of when Rianne says "they would catch fire and burn the cauldron" in chapter 76.
If Quirrell used the diary to resurrect himself, as it certainly seems like since Harry can touch it, and what he says about memory imprints is true, then Quirrell has the mind of a sixteen-year-old. A sixteen-year-old psychopath at that.
The Interdict is a very good reason to make people immortal.
In chapter 74, Quirrell describes an old and terrible ritual, one intended to summon up Death - involving a noose that has hanged a man, and a blade used to kill a woman. He mentions offhandedly that the ritual to counter this has been lost to time. This sounds remarkably like the cause of the Dementors...
If horcruxes work the same way as in canon, then someone has been horribly murdered while in the presence of the Pioneer plaque and the deed has been covered up afterwards.
All of the crazy stuff Harry pulls off is done in his FIRST YEAR. What could he be capable of in his second year? The third? The fifth?
How is this Fridge Horror? If he's this awesome in his first year, think how exponentially awesome he will become as he grows up.
For that matter it's been discussed in the text.
Chapter 28, where Harry finds a loophole in the laws of transmutation to change part of an eraser to metal without changing the entire thing due to a branch of what boils down to multiverse physics. Even if it checks out on the magic side of the equation, there is no way to know what would happen once the spell wears off naturally, since it works with a probability-based science turned constant on an infinitely improbable situation, and the realm of consequence for messing with what could have been over time stretches from nothing major, to radiation poisoning, turning Hogwarts into a flaming crater, or tearing the universe atwain.
Or it could simply revert to be a normal eraser. As we can infer from the fact that the universe has not yet exploded and yet partially transfigured substances have been left lying around.
When Draco is briefly forced to consider siding with Dumbledore, he decides he'd rather be burned alive. And then when you read it again with the knowledge that Draco believes Dumbledore killed his mother by burning her alive while she slept, that comparison becomes rather horrifying.
And very similar to the decision that the Potters took — dying rather than letting Voldemort kill Harry.
The story indicates that teachers can freely use memory charms on students without oversight or appeal (after the ritual incident, Snape modifies over a dozen students' memories without the Headmaster's knowledge). While we haven't seen any actual abuses of this, there have been tales of Defence professors who really get around or are more Obviously Evil than Quirrel, and if, like Snape, they can do it without Dumbledore's knowledge, the implications are not pleasant.
Let's be honest, Methods spends half its time examining the unpleasant implications of Rowling's magical world, such as the horrors of Azkaban, the corrupt and feudal nature of wizard society, and its distain toward non-wizards.
Those weren't "implications". They were major themes of the series.
If they were major themes then perhaps they should have been discussed in some way. Very little of canon!Potter is concerned with the corruption of the Wizarding World. That's just the backdrop against which the story unfolds. The closest Rowling comes to confronting it is, perhaps, SPEW, and that's (quite rightly) treated like a colossal joke.
If Harry's theory about how Fred and George pranked Rita Skeeter is correct, then Fred and George were able to False Memory Charm her and get away with it. The scale of the pranks they (or less honorable people) could effect with that method are frightening. Which, in hindsight, actually makes it a bit heartwarming that they erased the knowledge of how they did it.
Alternatively, they actually paid someone else to cast the False Memory Charm, which may mean that there is a criminal out there that does this for money. Making it horrifying again.
Given that Dumbledore 'drops' a valuable magic item near them soon after, one can imagine that HE either memory-charmed Skeeter, or faked the evidence she saw.
"Miss Granger," Professor Quirrell said gravely, "it can be dangerous to give people compliments like that when they have not been truly earned. The recipient might feel bashful and undeserving and want to do something worthy of your praise...."
And what happens in the next arc? Hermione dies horribly. Coincidence?
There are maximum two arcs left at this point, and in-universe it will all be over in two months – the end of the school year. Which means Harry will rip apart the foundations of reality before he turns twelve.
Or, you know, fail. Or there may be a Time Skip or something, of course.
Harry keeps insisting that he has never been abused, but I do think witnessing your mother get killed and then being hit with a strong, hate-filled, dark curse that is meant to kill you but doesn't, when you are fifteen months old, qualifies as child abuse.
Well, the next part of the conversation, where Harry discusses a time where his mother sends him out on an errand despite his worries about a serial killer, seems to suggest to me that Harry's Cynicism Catalyst was effectively his own intelligence and perceptiveness making him very much aware of humanity's flaws and how unsafe the world really is. A Deconstruction of Awesomeness by Analysis, perhaps?
If The Reveal in chapter 102 of the true functionality of the Horcrux spellis true, and the Pioneer Plaque is indeed a Horcrux then Voldemort has successfully fucked the Plaque's message of peace and introduced all of humanity as assholes to any aliens who find it, as whichever alien picks it up will get Mind Raped. Good Job Breaking It Hero
Of course, this will be a moot point if Harry nukes the universe, but if that doesn't happen, it might just cause a... diplomatic hiccup for the children's children. The kind that might end in an Earth-Shattering Kaboom.