Well after I got all worried about this, I decided to run my MBP on battery for a while to see what would happen.
It was a little disturbing to see it drop 3% in the first minute and a half after startup, but after that the battery behaved more sensibly. I went from 85% to 80% in about 25 minutes while doing not much of anything except opening and closing apps, turning the camera on (opening photobooth), etc..
So I shut down at 80%, waited a couple of minutes, and plugged in my power adapter, and the light turned orange after a few seconds, as usual. It looks like it's charging just like it always has.
I really hope there is nothing bad about Mountain Lion that can't be fixed, because I really like the OS. I hated Lion, but this release really surprised me. I wasn't expecting it to be slick at all, but it really is.