EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
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. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
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, ten.
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:
You do not need to rot13 anything about HP:MoR or the original Harry Potter series unless you are posting insider information from Eliezer Yudkowsky which is not supposed to be publicly available (which includes public statements by Eliezer that have been retracted).
If there is evidence for X in MOR and/or canon then it's fine to post about X without rot13, even if you also have heard privately from Eliezer that X is true. But you should not post that "Eliezer said X is true" unless you use rot13.
My running theory is because he's a horcrux, but it's hard to say. Apparently there's one point where this fix departed from cannon, if we can pin point that you'll have your answer.
Alright, fine. An actual non-sarcastic answer. He plays with the trope of being insane. He's entire chaos legion cackles maniacally. He is very certain of strange ideas that are almost the opposite of that his experienced elders believe, about their areas of expertise.
From that point of view it's easy to see why people would think he's crazy. Not to mention the simple fact that he doesn't adhere to social rules like normal people do.
The short answer is that this hasn't stopped Hermione from trusting him and considering him her friend before. And she did look at Harry later (once convicted) begging for help.
The only open question is whether there was something significant Minerva mouthed to her that we're not aware of. I consider this very unlikely.