This problem has several potential causes so here goes
1) The trailing arm on the offside rear suspension can be faulty (bent?!) which should be replaced under warranty if you have one.
2) There can be a cross threaded bolt holding the trailing arm plate, where it is fixed to underside floor-pan captive nuts. This can working loose. The first 50% from the head is threaded then a plain indented ring section and the leading third threaded but with three equally spaced scallops parallel to bolt shaft -apparently a self cutting bolt.
3) The drivers side rear exhaust may needs shifting slightly - I had this on my car, my dealer fixeded it 20 minutes after I took delivery!
4) The noise can be caused by the rear brakes. The ZT260 uses the same brake callipers at the rear as the front of my Elise, which have a tendency to get rattly brake pads, especially as you pull away giving a clunk sound. You can get some sticky foam pads to fit to the callipers to fix this from eliseparts.com.
5) The dealer I use has alsoreported seeing a couple of cars with loose suspicion bolts and simply tightening them up has cured the problem.
6) I have heard of cars which have stood for
a while getting seized suspesion bushes which have worn prematurely and
had to be replaced.