Thanks for the replies. I first tried re-installing the Flash player; that didn't work. So I re-installed 10.6.1 via the combo update. That worked.
Incidentally, I've been going the combo update route for quite a while (since the time I had network problems after an update; combo update fixed that, too) but thought I'd try Software Update with Snow Leopard. Anyway, I think I'll stick with the combo update from now on.