I had made some changes to /etc/apt/preferences and did an:

# aptitude full-upgrade

A bunch of packages were upgraded to unstable, and the end result was that something in the upgrade made xscreensaver scream and die.

When executing

$ xscreensaver-demo

I'd get the error message telling me that the xscreensaver daemon wasn't running (even though I have it in my KDE Autostart directory) and would I like to run it, I say "yes" and then I'd get the error message telling me something to the effect that "xscreensaver daemon did not start up properly" and that I should check my $PATH.

Thus, xscreensaver wasn't working. But KDE's less-than-perfect screensaver did work. But since kscreensaver is not xscreensaver, it is, therefore, inferior, and not worth using....

I looked through the appropriate log in /var/log/ and noted that xscreensaver wasn't upgraded. Hence, the problem was not with xscreensaver but with something else that was no longer playing nice with xscreensaver. I noted that some xserver-xorg-* packages had been upgraded, and I guessed that the problem was in this particular set of upgrades.

My xorg.conf file had not been changed since July, so the problem wasn't in there. I didn't have any permission-related problems with respect to executing xscreensaver. I exhausted every possible configuration-related problem that I could think of. So, the problem had to be package-upgrade-related.

I took the lazy way out and downgraded both of the xserver-xorg-* packages that were upgraded to unstable back to testing. And the problem was corrected.

I'm not sure what the problem was, and I had not collected enough relevant information to write up a bug report on the problem.