m,
It looks like your Facebook Application configuration is not correct. Can you re-run the Autotune configuration tool in JFBConnect and ensure that the Website URL and App Domain are setup according to the recommendations? When you enter the FB App section, make sure you click the "Refresh" button to get the latest recommendations.
Right now, when I try to login, a Javascript console message is shown that says:
Given URL is not allowed by the Application configuration.: One or more of the given URLs is not allowed by the App's settings. It must match the Website URL or Canvas URL, or the domain must be a subdomain of one of the App's domains.
I think if you fix your FB App, the login functionality should start working properly.
Thanks,
Alex