Safari can't verify the identity of the website errors

In my opinion you are missing an important root certificate. As a result the certification chain is incomplete and the intermediate certification authority thawte DV SSL SHA256 CA can't be verified.

To restore the default content of /System/Library/Keychains download the OS X 10.8.5 Combo Updater. You may either install it or extract the files. If you have reasons not to update to 10.8.5, additionally download and install Pacifist. Open the image OSXUpdCombo10.8.5.dmg. In the mounted image open the file OSXUpdCombo10.8.5.pkg with Pacifist. Then install them by choosing the three files in the keychain folder and hitting Install (red circle).

You need admin privileges to do so.

This might not solve your problems immediately but you got all the Thawte certificates back and start over resolving your issue.

Additionally I advice to update to OS X 10.8.5 and install any supplemental updates for 10.8.5 and the newest security updates: Security Update 2015-006 Mountain Lion.