To start with.... I'd recommend raising every character's age by a few years. (I think this is a 'love-it-or-hate-it' idea, but I have no clue how prevalent either of these viewpoints are... How many people think that the first-years really act like eleven-year-olds? And I'm not just talking about Harry...)
And, consequently, Hogwarts now has only four years.
Also, I'm clueless about the math, but... I seem to remember reading in a discussion thread that 1000 students in Hogwarts implies a total wizarding population the size of a small town. So I'd cram in 4000 students into the 4 years of Hogwarts. (We're gonna need TAs now, but that doesn't change anything fundamental.) Unless... The population is still too small, in which case... I suppose you could keep the 1000 students and have other wizarding schools.
And I'd suggest compressing the first four chapters into one.
ETA: Also, partial transfiguration. Harry shouldn't get it right that quickly.
Claims of "No kids act like that!" where I've personally been or known kids who act exactly like that have made me very suspicious of the general pattern. Harry probably acts just like Eliezer did, or would have if he'd already known about Bayes.
Warning: As per the official spoiler policy, the following discussion may contain unmarked spoilers for up to the current chapter of the Methods of Rationality. Proceed at your own risk.
Assume HPMOR was written by a super-intelligence implementing the CEV of Eliezer Yudkowsky and assorted literary critics. What would it have written differently?
... is what I want to know, but that's hard to answer. So here's an easier question:
In what ways do you think Eliezer's characterisations/world-building/plot-fu are sub-optimal? <optional> How could they be made less sub-optimal? </optional>
(My own ideas are in the comments.)
To put it another way... Assume a group of intrepid fanfic writers in the late 2020s are planning to write a reboot. What parts of Eliezer's story do you think they should tweak?
And just to make sure we're all on the same page: Eliezer isn't going to go back and change anything he's written to bring it in line with anything suggested here. This is purely an "Ah, just consider the possibilities!" thread.
... which means that we can safely suggest drastic rewrites encompassing 30 chapters or something. Or change fundamental facts about the world.
(Exercise due restraint on this one. Getting rid of the Ministry/the Noble Houses/blood purism would probably turn the story into something completely different; this isn't what we're trying to do here.)
With that, let the nit-picking begin!!