(see the CertWatch website for a detailed description of the CertWatch Addon. Please ask questions at the CertWatch website; the Review facility below is for reviewing the addon only, not for support.)
When Firefox with CertWatch runs for the first time, CertWatch reads and records all available root certificates, in CertWatchDB3.sqlite (in your Firefox Profile directory). It can take up to 30 seconds to create the SQLite database.
When you visit a secure website (an 'https://' website), CertWatch informs you if the certificates have been encountered before or if there are new. New certificates for a website visited before is an indication that something needs careful examination.
You can specify in the Preferences whether you want notifications only for the first time a certificate is encountered, or more times.
In addition, CertWatch saves an entry for each HTTPS connection. Although we do not use this information yet, you can read the CertWatchDB3.sqlite database file (stored in your Profile folder) with your favorite SQLite editor and read the details. See SQlite Manager or run sudo apt-get install sqlitebrowser in Linux.
CertWatch is internationalised, so you can start localising (translating) in your own language. Start translating CertWatch at the CertWatch Babelzilla page.