On both my computers running Mac OS 10.10 and my son’s computer running Mac OS 10.11 our major browsers (Firefox and Chrome) have in the last few weeks been disallowing an increasing number of https connections because the certificate is signed by an untrusted authority. AVAST is listed under authorities in Firefox. I also tried exporting the certificate from Firefox and adding it manually to the user directory where FF looks for certificates. An AVAST certificate was listed in my keychain, but turning on enterprise roots in Firefox didn’t help. Sometimes a site breaks without throwing off any kind of error message (e.g. parts of healthy.kaiserpermanente.org don’t work but no security error is generated, only “service is not available at this time”) My only recourse is disable webshield altogether, which is an pain because it requires multiple steps and an admin password.
On one of my machines I tried reinstalling both AVAST (free version) and Firefox - no joy.
Mozilla’s only recommendation is to disable web shielding altogether.