If it is an aftermarket clutch setup, I'm going to guess that pretty much any noise/chatter you hear is perfectly normal. Even the stock clutch chatters a fair amount when sitting in idle - it's very easy to hear it sitting in my garage with the windows down. Joe at ZSpeed offers a noise dampening option with clutch kits he sells to folks that DD their Z or just don't want the excessive chatter.
Personally, I enjoy the chatter. I'm looking forward to replacing my clutch and getting a super lightweight flywheel that will likely have my Z sounding like an F250 diesel at idle
