I'd imagine one problem would be simply maintaining the members...
Who is in charge of membership? Who decides if Johnny - who hasn't logged on for two months - should get kicked from the group?
Who's going to decide Bob is being counter productive by purposefully undermining the groups achievements?
I've wondered about these issues myself. In my head I like the idea of groups working akin to a local faction in a station. Anything they do at that station benefits their position at that station (eg: trading or cashign in bounties). As their position improved they could dominate the local system and actualy take ownership of the local station(s). At that point their group/faction could then become a viable group/faction at neighbouring stations where the same process would begin there. So in effect they have a bubble of ownership/effect.
What I could never rationalise in my head is... why? There would need to be some sort of reward ultmately. eg: For any station they own, any visiting CMDR (& pretent virtual NPC calculated on station business) pay small docking fee (eg: 500CR), and that is then spread across all members etc... So if a group take over a busy station they could bey getting a nice regular income. But other groups could then take an interesting in taking the station over etc...
But I always saw too many issues/problems with any mechanics I could come up with
I always liked the idea of my group of friends trying to become a viable faction/group in a little station and getting a nice little financial reward from our efforts as other CMDRs passed through/used it.