I suggest allowing more than one Group Moderator per Usergroup.
As you know, the responsibility of the Group Moderator is to accept/deny group membership request.
Problem is, if the designated Group Moderator for some reasons is unable to login to the forum for some time (e.g., he/she has to go to some place where there's no Internet connection), then the requests will be delayed, and users will complain.
To prevent such problems, there should be more than 1 Group Moderator per Usergroup. This way, if one Group Moderator is unable to login, the other Group Moderator will be able to take his/her place. Complaints from users feeling they're being unfairly delayed will drop.