Huw,
Because your site is new, Facebook likely hasn't scanned it yet. I'd recommend enabling the Open Graph integration in JFBConnect's Social configuration area, which will do most of the work for you. Then, as Facebook sees your site (through normal page visits), it will start clearing up the issue.
As a test, I liked the page below with one of my user accounts. Then, I logged in with a different Facebook user and saw the issue:
www.forevertangles.com/words/product/show/8-jessica-a4
Then, I used the Facebook Linter, which forces Facebook to scan your page, and then I was able to Like it with the 2nd user. The linter can be found:
developers.facebook.com/tools/lint
Hope that helps explain. Even without Open Graph enabled, this will start clearing itself up.. but basically, it's Facebook checking to make sure that the page being liked isn't spammy, malicious, or generally unknown.
As for the redirection on registration, what menu item do you have set in the Login/Logout Redirection section of JFBConnect? Is that a valid menu item to redirect to? If so, what SEF extension are you using on that site?
Thanks,
Alex