It took some time and testing to realize that there is a broken aspect of the Group's interface. The lack of documentation for the new Group's feature set would have revealed this problem very quickly.
Expected behavior: When you invite someone to the group you have the option of selecting their role and title at that time. As I understand it through working with the interface through trial and error and a concise answer from Kelly Linden, not documentation, the role is a collection of abilities assigned to the role and the title is the namesake of that role. The title is seen in the list by the group members and by the public and it is seen above the avatar if that is the choice of the user and that group is active.
Assigning the role and title at the time of invitation works, assigning it afterwards does not.
Current behavior: As I said everything works at the time of invitation. But if you need to reassign a role and title after invitation and/or create a new one later, only part of the action takes place.
Under the General tab the new assignments' title does not appear, just the default "Member", this is also what appears over the avatar's head. Under the Members & Roles tab, Roles sub-tab it will accurately show the correct amount of members in the group, so in a sense that part works, as far as I can tell. Also under the Abilities sub-tab the interface seems to accurately show the right ability assignment.
I have tried re-inviting and that works but that is not a practical solution for large groups. No amount of de-assigning and reassigning and/or refreshing from server changes the situation.
Like I have said in the past and will continue to repeat in the future until its rectified, proper documentation of Second Life's interface, tools and features brings these issues to light much quicker as it allows a template of comparison between expectations and results.
Documentation is also great marketing in that it shows off what something does, gives the user and potential user the epiphanies that excite creative activity and builds trust and loyalty in the product. Needless to say, it sure cuts down on user sarcasm and the huge load on help, support and posts in the forums.