Ahh, I didn't think to look at the open bugs because it just hit us. The screen capture in 43686 looks exactly like what we saw. Here I thought I was giving advance heads-up (and so proud of our one-hour problem->resolution timetable) when in reality we're just way behind.
We're still running 6.0.5, although we have been for several months now. There were no recent upgrades, no recent restarts, or anything similar. I'm not sure what triggered it so late in the game.
The only commonality was that it appeared after a full Firefox restart for each user, but we've restarted our browsers since the upgrade too.
What's interesting is that the 'beach' theme worked fine in the admin interface, but wouldn't work if the user logged in on their own (even in the same browser).