Flickering textures

[[ SOLUTION BELOW ]]

Hello! Bug report I'm afraid.

For the first 15 minutes or so everything is peachy, but then textures start flickering on update, as in these:

http://imgur.com/3GZGg.jpg
http://imgur.com/qPp18.jpg

If I wildly swing my mouse around, it makes things visible. The order seems to be:

* mouse moves
* draw goes okay
* draw gets covered up

I've tried turning off shadows, and it persists across restarting the game and the computer.

Interestingly, it seems to change something outside the game. Quitting and starting it back up sees the problem appear immediately. Even while playing other games: entire objects will appear to be missing and occasionally flicker into existence before disappearing again. Restarting fixes that.

Any ideas?