Sooner or later I will have to make a permanent move from Windows XP to Windows 7. I have a spare hard drive for this sort of experiments, so I transferred my settings to it with the wonderful Windows Easy Transfer and watched to see what might break.
Sure enough, Vim promptly lost the ability to write any backup files (the ones with the tilde after the extension) into the temp directory as I originally intended. I'm not sure how to fix this, so I cobbled together the workaround below:
First, I figured that Vim's sudden inability to write to the temp folder must have been caused by this UAC stuff that started in Vista and annoyed a bunch of people at the time, so I went and disabled it with help from here. That did the trick, but with the side effect of neutering the "Edit with Vim" context menu entry: clicking on it would simply remind me to put gvim on the PATH, and then keep doing so even after I did add "C:\Program Files\Vim\vim72\" to the PATH. The context menu, by the way, is what you get when you right-click on a file name.
So, I had to tinker with the registry. That took three steps: first, back up the registry as explained here; next, eliminate the unresponsive "Edit with Vim" entry from the context menu as explained here; finally, add a working "Edit with Vim" entry to the context menu as explained here.
So far, it doesn't look like I wrecked anything. Vim is as good as I remember it from XP. It can run Stata do-files with my old settings out of the box. Next up: Subversion and TortoiseSVN.