Firefox dialog: unable to verify the identity of ... as a trusted site

Hi folks

I occasionally get the "unable to verify the identity of ... as a
trusted site" dialog when accessing a website using one computer but
not when using another. For example I like to look at the courses
available at "The Teaching Company" (at www.teach12.com) and get this
dialog when I'm about to log into my account at that site.

My questions are about the "Examine certificate" button in that
dialog. What I wanted to know is, when I get this dialog, is there
something I could look for in the certificate to determine if I should
proceed or not? Let's say that the certificate was used by some
spoofer to try to fool me to a site that is not www.teach12.com. Would
I in this case see something else than "www.teach12.com" in the
"Issued to / Common name (CN)" field?

And does anyone have any books/websites that they can recommend that
explain these issues?

thanks in advance,

JJ