Your Facebook application should be setup as:
Site URL:
golden-key.org/
Application Domain: golden-key.org
At first, from your description of working for you and not others, I would have said that you either have your Application in Sandbox mode or you had setup a white list of users that could access it. However, then I tried to register, and I was able to without issue.. as well as logout and back in again. So, it's not either of those.
So, I'm a bit unsure what's going on. With the FB user account you have, the login popup that comes up simply says "An error has occurred", correct? That usually indicates a FB application configuration issue, but that wouldn't be specific to only some users.
I also didn't see the lag you mention or the problem with the SCLogin's logout button after logging in with my Joomla credentials.
I did test with Chrome on a Mac, but I don't think that Windows would show much difference (I can try later though). I scoured the page's HTML for normal conflicts or other issues, and couldn't find anything. If you have any more information you can share, that'd be great. Otherwise, I'll test with Windows shortly, but I'm really not sure what the ultimate answer will be.
Alex