If all goes well, you shouldn’t notice a thing.
Update on 12/02/2006: Well, it wasn’t seamless, but it could have been worse. The DNS changes took some time to propagate, so I couldn’t actually get to the site on the new server until this morning. When I finally did, it was terribly slow, the home page was displaying posts from October instead of the current ones. I knew how to fix the issue, but because of the server performance problems (I’m still not sure if they were related to me or not), it took a really long time for the changes to save. Everything looks great now though, and the site seems speedier than ever.