We are using the Facebook connect plugin on liveviewlcf.com and are seeing a couple of issues.
1. When registering using Facebook, it creates the WordPress user but doesn't seem to associate it with the facebook account, you have to log in using the auto generated password and connect your account to facebook through your profile.
2. Once you have done that and you login using facebook, you are unable to logout.
You're more than welcome to register and account on liveviewlcf.com is you want to try to reproduce the issue yourself.