I just tried to register on your site using Facebook. I was properly brought to the JFBConnect registration page and my first name was shown. So, connections with Facebook do seem to be working.
However, when I tried to register, I was redirected to the Joomla registration page with the message "The words you typed did not match the ones displayed. Please try again." It sounds like you have Captcha enabled, but it's not properly displaying on our registration form. Can you try disabling Captcha in the User Manager -> Options area, temporarily, and see if that helps with registrations? Alternatively, you can enable the Automatic Registration process in JFBConnect so the user doesn't have to fill out any forms.
Finally, you look to be on a pretty old version of JFBConnect (v4.2). JFBConnect v4.3 was released late last year and v5.0.1 is the latest. I'd highly recommend upgrading as it's possible you're also running into a bug that's already been fixed.
Thanks,
Alex