I don't have direct experience with the NSX, but on a previous car I owned:
I was told that the car would stall sometimes if I free-revved the motor. The theory was that the revs would drop so fast that the ECU wouldn't be able to "catch" the revs from falling below whatever RPM threshhold that the car would stall at. This never happened.
I was told that the car would lose some drivability. The theory was that the momentum of a heavier flywheel helps keep the motor spinning while you're trying to minimally slip the clutch for a smooth engagement and start from a dead stop. I never experienced such difficulty.
Lastly, I was told that because the revs drop faster, that shifting smoothly becomes difficult because the revs drop too low while you shift. In other words, if it takes you two seconds to shift, and you're used to where the revs fall in the next gear, with the lightened flywheel, the revs fall drastically lower than what you're used to and you either have to learn to shift faster or kinda keep your foot on the gas a little to prevent the revs from falling too low. I got used to this during the first drive after the install by just shifting a little faster.
In my experience, though not on an NSX, the benefits of the lighter flywheel that you hear were all present with none of the bad things you hear ever becoming apparent.
Just my experience, another data point, my two cents.
J