Something is corrupting data between the web servers and my client. The most obvious symptom of this is that userpics and picpix/pics.lj images are getting distorted, but it's also corrupting the gzip-encoded data streams on journal views and causing pages which have all of the right characters but in the wrong order. It's intermittent, though; refreshing usually fixes it or at least changes the nature of the corruption. Several other people have mentioned this, too.
Given the timing, I'm guessing the blame lies with the new network configuration.