I was seeing an SSL error in Safari 6.1.6 (8537.78.2) on OSX 10.8.5 when visiting a website, and the debug information provided from the developer tools didn't indicate the source of the issue. The issue was reported by multiple users of OSX 10.8, and was resolved for those users by restoring TLSv1 in the server configuration (config change at bottom of question).
The error message in Safari developer tools was
Failed to load resource: An SSL error has occurred and a secure connection to the server cannot be made.
In Safari, there was no additional information under the "Requests > Network" tab (which I saw referenced on other answers). The information there seemed to relate to loading the content of the error message rather than the original site.
What other methods, if any, could I have used to extract a "server lacks TLSv1 support" message from Safari 6 / OSX 10.8.x?
Additional background info: The change required to the nginx server configuration was this -
-ssl_protocols TLSv1.1 TLSv1.2; +ssl_protocols TLSv1 TLSv1.1 TLSv1.2;