Be wary of anything that is not quite right about the engine.
Do your research so that you know the max and min oil pressures, max oil temperatures and max mag drops. When you have a trial flight watch the engine parameters like a hawk. If the oil temp gets very close the max or the oil pressures aren't within max/min, ask some searching questions. If the problem could be fixed easily and/or cheaply, the group would have done so already...
Ask about the engines oil consumption. Ask when the plugs were last changed. Ask to see the group's accounts and all receipts held by the group.
An engineer can (and should) check over the aircraft irrespective of when it was last inspected and by whom. (Every inspection to date, on the aircraft I have a share in, has turned up a vital point which we all grateful to have found out about). But the engineer will not be able to examine the engine - be aware that you could be buying into a whole load of trouble, even if the rest of the aircraft appears fine - the engineer cannot see the wear on the engine components. Engine (and airframe) log books also do not always tell the whole story.
I would not recommend buying an aircraft with a recently overhauled engine. Until the engine has got 100 hours on it, it is too much of an unknown quantity.
Make notes of all the answers given to your questions, by any of the group members and your inspector.