Firefox cannot recognize certificates for well-known sites

Solution 1:

Please check the time and date on your computer. An incorrect clock setting (for example, due to an empty BIOS battery) is the most popular cause of such problem. The SSL certificates are valid only in a defined date range (from/to). If your clock has been reset, certificates are "not yet valid" :D

Solution 2:

In order for ESET Smart Security to examine the data inside an HTTPS connection for malicious behavior, it has to MITM your connection. However, how this usually works is that they install their root certificate in your browser's list of trusted root certificates, so everything looks fine.

This has several security downfalls, however, including potentially making all of your private Internet browsing decryptable by ESET Smart Security. Likely the installer configured the root certificates for Internet Explorer, but not Firefox, thus the errors. You can probably check their support site for how to configure their certificate properly if you want to analyze HTTPS traffic.