Check your rear diff bushing. If this has grease oozing out of it and looks cracked that means its time for a bush kit change. This gets rid of the well known shuddering on throttle from the rear end on all cars with this subframe (350Z etc). I recommend a whiteline or super pro bush kit which will tighten up things back there and feel better when launching or just general response.
please check the front diff driveshaft universals while you're at it . Mine shattered completely one year and requires rebuild - PNM35 3.5L
