Oops ... when I moved everything to the new server, I installed a new version of MovableType and just imported all the entries from our blogs from the old server into the new one.
In doing so, all of the individual archives have different file names. So now all the Google search queries are either landing on non-existent URLs or on blog entries that have nothing at all to do with the search query. On the other hand, given what some people search for when they find our site, they probably weren't finding what they were after, anyway.