Dag,
Not sure what's up with notifications, but keep an eye on things, obviously, and let us know if it stops working again.
As for the comments box, yes, Like buttons and Comment boxes do not require a Facebook ID. Having one does enable some extra capabilities like Facebook Login, Page Tab integration, and a lot of other JFBConnect features. It also makes it so that a tag we add to the top of each page that specifies the App Id notifies Facebook of the 'owners' of the page. Whoever is the admin of the app is considered an owner of the page, and therefore, can moderate comments.
Your page is actually including an Application ID (289658537766430), whether you actually need it for some of the features I mention or not.
So, here are a few recommendations that I have for your page, which should help get moderation going:
1) Find out who is the admin of the app with ID 289658537766430 and have them add you as an administrator.
2) In the Social -> Open Graph tab of JFBConnect, enable Open Graph integration. It looks to be off right now. This helps describe your pages to Facebook (title, description, etc) for posts in user's wall when the comment or like a page. Additionally, this adds more information about the owners of the FB Application. In the "Defaults" box on the same page, you can add your Facebook User ID as an explicit admin (even if not an admin of the Application), and the moderate link should then show. You can add the admins tag like:
Where 123456 is your Facebook User ID. If you go to your Facebook profile and hover over your avatar or name in the top left, the URL should have your ID in it, like:
www.facebook.com/profile.php?id=1251253607
Hope those ideas help.
As for the moderation tool not working, that may be because you aren't the owner of any apps. I've never heard of that problem and know that link works for most people just fine.
Best of luck,
Alex