My first car was a '90 300ZX TT w/ t-tops. I didn't have much exposure to the earlier models, but I did talk to a few owners at meets.
General things to look for on all 300ZX's are:
1) The t-tops are known to leak with age. Remove both and check the condition of the paint in the 'frame' that holds them in place. If you see any rust, then the t-tops have been leaky for some time.
2) If it is a turbo model, then expect to replace the turbo(s) at 120-140K miles. If not a turbo model, the NA Z's have been known to have engines that are generally maintenance free and can last well over 200K miles.
3) Z's also had undersized rotors, and warpage is common on all years (Z31 & Z32)
4) Make sure they're no open recalls. I think there was some kind of power steering recall as they leaked fluid...
Good luck!
-Chike