I visit a few known intranet locations that do not have proper certificates installed; therefore, I receive the "This Connection is Untrusted" notice.
In 3.x versions of Firefox, I could click the "Add Exception" button to add an exception and continue to the site.
In 4.x versions of Firefox, the "Add Exception" button simply doesn't work. There is no way to add an exception from the "This Connection is Untrusted" screen.
This features still exists, but I wonder whether a setting might be blocking it. Are you saying that if you click the "Add Exception" button nothing happens, the dialog does not open? Or the dialog opens but it doesn't work?
If you can't add an exception via the Error page then try to do that in the Certificate Manager.
When clicking the "Add Exception" button, literally nothing happens. No dialog or additional window opens. It is as if I had never clicked the button. I can click it 5,000 times and nothing happens.
I would be annoyed, too. Can someone who has this problem test in Firefox's Safe Mode? If that works, then an add-on probably is causing the problem.
I recommend backing up your Firefox settings in case something goes wrong. See Backing up your information. (You can copy your entire Firefox profile folder somewhere outside of the Mozilla folder.)
Next, try starting Firefox in Firefox Safe Mode. Be careful not to "reset" anything permanently if you didn't back up.
Does the button work?
It is possible that you can't add an exception if there are specific problems like in this case where there is a certificate that may have been valid in the past. You probably can't add an exception if the certificate has been revoked or otherwise got invalidated. Security gets stricter with every new Firefox version.