From what I've seen, I would say that the things beyond your control that will be most important in the long run in a group are:
1. Are that any issues with the other pilots in the group in terms of how they're flying the plane
2. Bad people relations within the group. The fact that you won't physically see them very often can lead to miscommunications
3. Availability of the plane. A degree of flexibility goes a long way and being fair
4. Degree of maintenance and who is carrying it out. Big potential issue.
And none of this will obviously be easy to find out.
It's a bit like thinking about buying a house and finding out if there are any issues with the neighbours.....you have to think laterally ;-)
In my experience, the best place to try and find out the truth is with the local flying club and its instructors. They tend to get to know this stuff and every time I thought about a share I was always able to find out the hidden story (good and bad) this way.
BFA