The order of installation seems to matter. Installing Gnash, and then
(re-)installing Flash caused most embedded videos to play properly. I
have not tried Flash-based UIs, like Flash games.
To put the nail in the coffin of this, after a lot of experimenting,
visiting numerous web sites with Flash, Gnash just isn't going to cut
it, so I:
1. Purged flash-plugin-nonfree
2. (Somehow) removed the gnome metapackage without having half my
installed packages go with it
3. Removed gnash and mozilla-plugin-gnash (but left gnash-common in place)
4. Installed flash-plugin-nonfree
Now everything works. Except Plants vs. Zombies. Bejeweled 2 works,
though. :)