I'm a bit surprised that nobody has started talking about one of the most important things revealed in this chapter. Quirrell knows that Snape is on Dumbledore's side. The fact that they had a double agent working against Voldemort in the original canon was quite possibly the Order of the Pheonix's single biggest advantage, and in this canon I would say that it was one of the two most important pieces of information Quirrell might not have known (the other being that Harry knows about the prophesy.) This solidifies Quirrell's position tremendously; there are few liabilities greater than an uncovered double agent.
He's Quirrell. I more or less assume Quirrell can deduce at least a cynical caricature of any player's motives, resources and actions with a glance or two. Snape trying to double agent Quirrell and Dumbledore just seems absurd!
I'm also not sure I would quite have assigned Quirrell as the guy who needs to know about Snape's loyalties. It seems like it is Lucious who is going to be the Death Eater Lord in this one. Quirrell has a whole other game. This means that Snape still has a chance to be a double agent, so long as Quirrell doesn't meddle for fun and/or profit.
Update: Discussion has moved on to a new thread.
The hiatus is over with today's publication of chapter 73, and the previous thread is approaching the 500-comment threshold, so let's start a new Harry Potter and the Methods of Rationality discussion thread. This is the place to discuss Eliezer Yudkowsky's Harry Potter fanfic and anything related to it.
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. The fanfiction.net author page is the central location for information about updates and links to HPMOR-related goodies, and AdeleneDawner has kept an archive of Author's Notes.
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: