Many of these don’t exactly count as Chekhov’s guns, but they have this in common with your Chekhov’s guns: They seem like substantial unresolved things and I will be disappointed if the end of HPMOR leaves a lot of them unresolved:
Prophecies about Harry and the end of the world (for some values of “end” and “world”).
How magic works (e.g., why you have to say “Wingardium Leviosa” to make things float; resolving this may be more or less equivalent to resolving spell creation).
Harry’s intention of defeating death, perhaps in some fashion that involves the Deathly Hallows.
The list of locations discussed by Harry and Quirrell, which may or may not correspond to Horcrux hiding places or something.
Harry’s “power that the Dark Lord knows not”; probably not either Science or partial transfiguration, but unlikely to be “love” as in Rowling.
What’s wrong (and how genuinely) with Quirrell.
The interaction between Harry’s and Quirrell’s magic (kinda the same as in Rowling? maybe, or maybe not).
Harry’s vow to do away with Azkaban and the use of Dementors to guard human beings.
Harry’s debt to Lucius Malfoy. (Or—I forget—did that get cancelled somehow when Hermione got killed?)
What, if anything, Harry was doing after Hermione’s death; e.g., is he carrying her transfigured corpse around or something?
Harry’s “father’s rock” (just transfiguration practice? actually some powerful magical artefact in disguise? etc.)
What really happened in Godric’s Hollow when Harry was a baby.
Exactly what Quirrell’s plans really are. (On some plausible theories, closely related to what happened in Godric’s Hollow.)
Many of these don’t exactly count as Chekhov’s guns, but they have this in common with your Chekhov’s guns: They seem like substantial unresolved things and I will be disappointed if the end of HPMOR leaves a lot of them unresolved:
Prophecies about Harry and the end of the world (for some values of “end” and “world”).
How magic works (e.g., why you have to say “Wingardium Leviosa” to make things float; resolving this may be more or less equivalent to resolving spell creation).
Harry’s intention of defeating death, perhaps in some fashion that involves the Deathly Hallows.
The list of locations discussed by Harry and Quirrell, which may or may not correspond to Horcrux hiding places or something.
Harry’s “power that the Dark Lord knows not”; probably not either Science or partial transfiguration, but unlikely to be “love” as in Rowling.
What’s wrong (and how genuinely) with Quirrell.
The interaction between Harry’s and Quirrell’s magic (kinda the same as in Rowling? maybe, or maybe not).
Harry’s vow to do away with Azkaban and the use of Dementors to guard human beings.
Harry’s debt to Lucius Malfoy. (Or—I forget—did that get cancelled somehow when Hermione got killed?)
What, if anything, Harry was doing after Hermione’s death; e.g., is he carrying her transfigured corpse around or something?
Harry’s “father’s rock” (just transfiguration practice? actually some powerful magical artefact in disguise? etc.)
What really happened in Godric’s Hollow when Harry was a baby.
Exactly what Quirrell’s plans really are. (On some plausible theories, closely related to what happened in Godric’s Hollow.)
And that curse Quirrell mentioned that requires a sword and a rope. I think it will have to do with Bloody baron and the Monk (House ghosts).