A couple of ideas:
(1) There is a strong need for group administrators within ArcGIS.com to be able to control / moderate content that is shared with a group. They should be able to set these parameters (e.g., when sharing a map or service, a dialog box will appear to notify the group member that they cannot share content with this group because they do not have admin access).
(2) Group administrator can receive emails when people request to join group.
You guys could learn a thing or two from Facebook and the way that groups are organized and controlled there.