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!!
I always assumed, when reading the original books, that other British magical schools existed and Hogwarts just happened to be the best of them. The society as presented simply doesn't make sense otherwise, even accounting for the fact that wizards seem to live significantly longer than Muggles and don't seem to have many more kids.
It does take some handwaving (how would Hogwarts choose which magical children to send its acceptance letters to?), but not as much as fitting what looks like some pretty robust commerce and a rather heavyweight bureaucracy into a population of at most thirty thousand or so (less, if you extrapolate from class sizes).
Given that they canonically keep tabs on underage witches and wizards with magic, I suspect that they judge based on some combination of how magically promising the prospective student appears to be, what their social connections are (are they related to any highly placed individuals who graduated from Hogwarts?) and possibly some sort of affirmative action for muggle born students.