So interesting. I'm going to PM you a Facebook application keys. If you could, please try them out in JFBConnect and see if you get the same error. This will help quickly narrow down the problem as to whether there's some odd setting in your app or whether it's something with JFBConnect in general. A screenshot of the settings will be attached to so you can try to match them up with your app, in case it works.
While we were setting this up, we did get an "Application error" dialog box. After we got this, we removed the Base Domain name and it worked fine. We haven't seen this before, but this was also working on our localhost development server, which can sometimes cause it's own issues. Facebook likes pages it can actually 'see'.
As always, report your findings. PM coming in just a moment.