That's strange. Works for me just fine in FF 28. The Panopticlick is rather old, though. Only thing that's useful about it is the stats about other browsers that have the same settings.
has more tests, including the new super-easy-to-use canvas fingerprinter. Using the HTML5 canvas object, it draws a moderately complicated image (text plus shadow with multiple fore- and background colors), then gets a browser generated checksum of the image. It's an exercise in software, graphics library, and hardware interaction.
------ did not even get prompted for an unsecure site at Panopticlick
I updated one of my machines to FF29, which you show as the browser causing problems, and was still able to visit Panopticlick without getting a certificate warning.
Did you do something like flag their certificate authority (Startcom) as distrusted?
Preferences -> Advanced (tab) -> View Certificates (button) -> Authorities (tab) -> (alphabetical list of authorities, and sublists of certificates from those authorities) These are the general CA certs.
Preferences -> Advanced (tab) -> View Certificates (button) -> Servers (tab) -> (alphabetical list of authorities, and sublists of certificates from those authorities) Certs that have been explicitly trusted or distrusted will be here. For example, I've got an AT&T Web Scraping Proxy here as explicitly trusted for one host, and seven Diginotar certificates as explicitly distrusted for all hosts.
------ for whom opening "View Certificates" took quite a while