Facebook API Error: An unknown error has occurred.

Sergiu,
Try the following:
* Logout of Facebook.com
* Go to your site and click the Login with Facebook button
* Try to login with a Facebook account that is an administrator of your Facebook Application (not necessarily an admin on your Joomla site)
That should hopefully show a better error message.

If not, please go into Autotune in JFBConnect and:
* Go to the FB App section and hit 'Refresh'. Make sure your settings are all up-to-date.
* Run the Error Check tool to look for any issues.

I hope that helps, but if not, let us know, and we can investigate further.

Thanks,
Alex