The upgrade went smoothly, and I now have the latest version of Movable Type running on the server. This means obscure new features! Woo! (You might notice some improvements.)
I tested comment posting and it worked without error this time, so hopefully it was an MT problem solved by the upgrade, and not a problem with my hosting service.
But that's enough work for one day. Someone bought me a copy of Anachronox earlier. Time to play, I think.