Thanks for the credentials. I just got into the site, and really didn't see too much out of the ordinary. So, I enabled the JFBClogin module you had made (in the right side) and tried to log in. I was brought to the Login/Register page, filled out my username and password, and everything worked as expected. I never saw the error you mentioned. The JFBCLogin module is currently back to disabled.
Of course, that doesn't mean your crazy. There are some things I noticed on your site that you may want to play with, and some other suggestions are below:
1) In sh404SEF, I set it to 'skip' creating pretty URLs for JFBConnect. We only have one URL, and that's the login/register page, and it's not something that needs to be pretty. This is the only change I made on your site.
2) You have a plugin for the Wibya toolbar enabled. I didn't see that bar, but it's caused issues on other sites because of it's Facebook integration. I would recommend disabling this, or at least disabling the Facebook features (Like/Send, etc) of that toolbar.
3) jBotelo, a minifier compressor is installed. We work with jBotelo, and many other compressors, but for debugging and sanity purposes, I would recommend disabling this for now as well.
Another thing to look out for: When you click the Login With Facebook button, and are brought to the next page, you should see "Welcome Bob", or whatever your first name is, at the top. Also, you have it set to hide email addresses, so you shouldn't see the email address field in the form. If your first name, or the email field is showing, that could be a sign that JFBConnect isn't properly pulling your profile or communicating with Facebook. In that case, I'd recommend:
1) Trying a different Facebook user to login with
2) Trying a different browser, at least, and different computer if possible.
Finally, in no way should you ever see that error. We messed up, and I have a note in our bug tracker to test better for the creation of the user and fail more gracefully. Sorry you're running into this issue, but we will get you fixed up.
You can disable my account for now, until I hear back from you at least
Alex