Hat-and-Cloak is Voldemort but not Quirrell. When in Quirrell, Voldemort has a whole (probably quite powerful!) brain to run his computation on. Outside of Quirrell, he relies only on what computation he can do purely as a 'ghost', or as magic, or whatever. Hat-and-Cloak is thusly disguised because Voldemort lacks a body. Or maybe Voldemort possesses someone else, who isn't as smart as Quirrell, and is proportionally dumber and more prone to mistakes. Quirrell is zombie while Voldemort's away because Voldemort set it up that way. Don't want your robot walking away without you.
Part of the groundhog-day attack involved setting up a trigger in Hermione, that when she can attack Malfoy, she should try to kill him. This explains her behaviour in the battle, and her apparent behaviour in the duel.
Hat-and-Cloak is a player in this story. Players in this story are clever and powerful. A sensible way of resolving this apparent contradiction is to postulate some form of disability or restriction applying to Hat-and-Cloak. Then all you need is Conservation of Characters.
What evidence is there that H&C isn't just Quirrell wrapped in an illusion?
There's no need for Hermione to have cast the lethal hex. She wins the duel, then the real perpetrator stuns both of them, hexes Draco, and then memory charms Hermione into thinking she did it. However, if that's the case, unless the perpetrator then used Hermione's wand to cast the hex, checking what spells her wand had cast would reveal something fishy.
Why are we proposing the H&C is not clever and powerful?
(The HPMOR discussion thread after this one is here.)
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. There haven't been any chapters recently, but it looks like there are a bunch in the pipeline and the old thread is nearing 700 comments. The latest chapter as of 7th March 2012 is Ch. 77.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes.
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: