Initial impressions:
There are really a lot of instances where the same photo was used for multiple images. That should probably be fixed.
There are a lot of requests for js and css files. If they're coming from your server, you should bundle them up into one file. Better yet, sources like jQuery should be coming from a CDN like Google for these reasons. Your webdev should check out Yahoo's website about performance if they haven't already.
The carousel on the front page is something that IMO should be expunged from the web. Replace the "slide left" behavior with the "fade in/out" used on the "What we do" page, for a good start.
The URL should be appliedrationality.org, not www.appliedrationality.org. http:// already tells you that you're looking for the web server. The redirect should go from www.appliedrationality.org to appliedrationality.org, not the other way around. Obviously, links such as the logo should be changed to match.
The pages look pretty terrible on my phone (Motorola backflip running Android using built-in browser). A lot of the text disappears off the right side of the screen. The header links should probably be formatted differently for mobile - the header section looks like a mess.
The page about mobile apps should have a note that they are "Coming Soon!" or something like that - I expect to be able to download the apps from that page, or at least link to descriptions.
The page about groups should link to some place where you can get in touch with a local group.
The CFAR link on the SPARC page looks like a tab, so it is surprising when it redirects to the CFAR website (ETA: Though this would not be the first website to use that pattern). Otherwise, nice use of CSS tabs. For some reason, the text on the SPARC page has massive amounts of whitespace in the source - you may want to trim it on the back end, though since you're sending resources gzipped it shouldn't make a real difference.
SPARC: GET http://www.appliedrationality.org/images/body.png 404 (Not Found)
The "What is Rationality?" page doesn't seem to have a clear answer to that question. Certainly not on a skim.
In general, great job.
In general, great job.
Quoted for emphasis.
The new Center for Applied Rationality website has launched! We'll be adding content as time goes by. Let us know if you find broken links, etc.