The hard and jittery ride is due to the fact that the car is not made for straight line performance and is more centered towards corning and touge.
This is an excuse for a poorly tuned
suspension. Lots of cars are designed to perform around a road course and the ride isn't harsh and "jittery." It might feel like a "real sportscar" to the uninitiated, but it's really just a sign of poorly matched components.
The early 350Z's suffered from rocking-horse motion over regular expansion joints and the "ripple" caused by truck traffic on concrete US highways. It didn't happen everywhere or to everyone, but pretty much everyone who had to drive on a road like that noticed the issue. It's been addressed somewhat with shock and spring adjustments, apparently.
A friend had a new 2003 350Z, and we'd drive on the same roads together at times. He hated certain sections of freeway because the front and rear of the car bobbed sickeningly at certain speeds, like 40 mph in heavy traffic. I would be following him and see it happen, while in my 99 Mustang GT the road was obviously rippled but the car ran flat over the ripples at 40 mph.
I'm pretty sure all year 350Z's have front tire wear issues because of
suspension movement and tire caster/camber/toe. Nissan recommended eliminating any toe out on the front tires as a "fix." Clearly the issue exists in the design of the
suspension, as other cars don't have this issue to the same degree.
I'm not saying the 350Z is a bad car and I wouldn't mind having one to flog myself, just that it isn't the
suspension superstar the harsh ride has led some people to expect. It's a very nice but imperfect car, like every other car on the road
Keep in mind that the 350Z was a totally new car for Nissan at the time. They aren't new to making sports cars, but the 350Z wasn't the pinnacle of a line - it was a brand new car that didn't have decades of refinement behind it. I'm sure the engineers at Nissan considered what mistakes were made on the 350Z and fixed them with the new 370Z.