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, in Act 4, Harry asks the twins for a plot, and the twins also discuss pranking Quirrell. In Act 5, the twins ask Flume for help, and show him an article in "yesterday's edition of the Daily Prophet", titled "THE NEXT DARK LORD?". In Act 6, Quirrell quotes that title when he confronts Skeeter; he also mentions he has no dark mark, which is one of the elements of the twins' discussion in act 4.
So at some point in the week between Act 4 (either Sunday or soon after) and Mary's room (Saturday), the twins convince Skeeter of certain things about Quirrell. The Prophet publishes the Quirrell article. At some point early the next morning, the twins ask Flume for help with Harry's article. At some point after that, and before Saturday, Quirrell confronts Skeeter on the street.
In summary, there's almost a week of lost time in chapter 25, which makes it a little difficult to see that the twins were behind Skeeter's article on Quirrell, but there are enough hints in there to make it a sure thing.
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: