Just to make it even more interesting, I was starting to get "denied" messages on Google Reader (why did I decide to go back to that application anyway?), so I decided to log out and log back in. When I clicked on logout, I get the warning from Firefox saying that the connection is untrusted. Looking at the technical details, things get even more puzzling:
www.google.com uses an invalid security certificate.
The certificate is only valid for *.s3.amazonaws.com
(Error code: ssl_error_bad_cert_domain)
Now my theory is that I have a misbehaving plugin on my Firefox. The odd thing is that I don't have many plugins installed, so I'm not sure which could be misbehaving. And if I turn one off, it required restarting Firefox, which might make the problems go away anyway.
Oh, well, I guess I'll just have to live with not knowing what happened.