My reading:
In 25 Harry asked the Weasley twins for help, and told them not to involve Quirrell in their plot, because he didn't like publicity. The Weasley twins agree, but are amused that Harry doesn't know them that well or he wouldn't have brought up Quirrell at all, and say they'll do Quirrell on their own time.
This part is never explicitly stated, but I assume they alert Rita to Quirrell and manufacture some silly rumors about him being a former Death Eater and training Harry to be the Next Dark Lord.
Rita then publishes an article making those exact accusations.
Quirrell confronts Rita about this. He pulls up his arm to show no Dark Mark. But she clearly shows she considers herself above all the rabble, doesn't give two damns about journalistic integrity, and simply doesn't care who she hurts. It is at that point that she thinks about Mary's Room, and turning into a beetle.
It is implied that Quirrell was reading her mind as she thought that, so now he has knowledge of her snooping habits and morphing abilities. He deliberately puns on this, saying that he now can't resist the urge to simply "crush" her instead. I don't think this first meeting was orchestrated by Quirrell, it was unrelated and simply gave him the knowledge he needed to set up her murder.
I deduce that Quirrell later leaks to her anonymously that he'll be meeting with Harry in Mary's room and something juicy will happen. I find it pretty damn delicious the way he toys with her without Harry's knowledge, she must've had a hell of a sphincter-tightening moment when he audibly considers casting a spell to reveal any animagi in the room. And it's awesome the way you (as a reader) don't notice that until your second read-through.
This part is never explicitly stated, but I assume they alert Rita to Quirrell and manufacture some silly rumors about him being a former Death Eater and training Harry to be the Next Dark Lord.
I agree — though it's hard to tell because chapter 25 is written out of order. But a week passes between when Harry asks the twins for a plot and the lunch with Quirrell when Harry reads the paper: Act 2 is stated as happening on Sunday; directly afterwards, in act 3, Harry talks with Draco and borrows 40 galleons, and sometime afterwards, probably directly after...
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: