There's a TVTropes discussion on this: Harry Potter Headscratchers
I might as well repeat the ones I put on there.
Shouldn't it be Harry Potter-Evans-Verres and the Methods of Rationality?
Why is Harry so death averse? He claims to be a preference utilitarian, but the sorting hat had no desire to live, yet Harry didn't want it to die.
Why does Harry reject the idea of Horcruxes? You can't save more than half the population, so it's hardly a permanent solution, but you could kill half of the people right before they die, and save the other half. This would work as a hold-over until Harry becomes God. Given my understanding of canon, this wouldn't actually work, but Harry wouldn't have no that yet.
In what way can a crime that hinges on an eleven-year-old boy be considered "the perfect crime"?
According to Wikipedia, timeless physics was discovered in 1999. If this takes place in 1991-1992, how does Harry know about it? Did he work it out himself?
To me the main reason of Harry rejecting Horcruxes is the "anti-Dark Lord Harry program". Harry is trying hard (and with relative success) to prevent becoming a Dark Lord, and rejecting a way to reach immortality for some at the expense of killing others is a way to refuse the Dark Lord path. Harry (in my view) doesn't fully trust himself to wield raw consequentialism, and he respects ethical injunctions like "murder is just wrong" (at least when he's just a 11yo boy and still afraid of becoming a Dark Lord).
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!!