FYI: It's not necessary to uninstall the 64bit version; as long as the 32bit version is installed last (
after the 64bit version), everything seems to go back to normal.
Also, this solved another minor but nagging problem I've been having for months - I use OpenOffice, and since the last time I updated that, I was unable to use the search function in OOo's help system. I don't remember if I also updated Java at the same time (let alone which order I installed the Javas the last time I updated them), but reinstalling 32bit 7u9 fixed OOo, too.
Thanks a lot, LotR.
P.S.: I've also adopted a policy of disallowing automatic updates of anything for my friends' computers (I'm something of the neighborhood geek-in-residence), but I didn't find any info about new or additional compatibility problems with this latest Java update. OTOH, I've pretty much banned Google Chrome on the PCs of anyone I do maintenance for, because of the difficulty of disabling automatic updates for it.