Assuming the aircraft passes muster (you MUST have at least one hour trial flight as P1 to put it through its paces for which I would expect you should have to pay) and is priced correctly the MOST important thing is the other members of the group. Make sure that you meet them all BEFORE signing up and feel that you can get on with them - find out how long they have been in the group and why they joined and what they think about it now etc
You can run groups two ways - a very rigid and strictly enforced "contract" to make sure that everybody does their bit (like cleaning the plane, making sure it is refueled after every flight, etc. etc) or you have a much looser agreement and rely on the reasonableness of the other members to do their share.
My group is of the latter variety and depends very much on trust between members which works very well.
Make sure that any booking system used doesn't allow other members to "hog" the times when you want to use the aircraft (e.g. I can only fly at weekends but two other members only want to fly during the week, so conflicts are almost no existent).
Also make sure that the finances are in good order and are run "transparently" so that you can see exactly where the money goes.
Two other pointers are :-
1. to be happy with are the process for selling youir share if you want (how is the price set for example) and
2. what happens if a major repair is required for which funds aren't available.
The basic rule is commonsense - if it looks too good to be true then it probably is.