Mark,
Yup, I was wrong. I think I tested on a different site yesterday. I just created an account on your site, and when I log in, I can see the 500 error. I've seen this before on a few other sites, and it's usually either a security issue where a firewall or other 'protection suite' is preventing the long URL that Facebook returns from being parsed and used on the site. The other option is that your Advanced SEF (which we're not as familiar with) is not liking the long URL.
If possible, can you elevate our account "sourcecoast" to super admin and we can investigate further. I'll install extPlorer, a file manager, to let us make some minor modifications to JFBConnect for testing purposes, and hopefully find the problem. If you have a development server to test on, that's always where we'd prefer to start.
Thanks for your patience, and we'll get you setup