When someone makes a comment using FBCComments on my website, I would like to have an alert when I go to my FaceBook home page (a red box on the notifications globe at the top, left of the page). I am the administrator for the FaceBook app that is used to moderate the comments.
That's not a feature that Facebook supports. JFBConnect does have a configuration option in the Settings -> Notifications area where you can set an email address that is notified on any new comments. That's the best suggestion I can offer for what you're looking for.
Hope that helps,