From personal experience shopping around for my Z.

Electrical:
-power window motors tend to go out
-rear taillight sockets tend to corrode on the '93-'97 models (I replaced mine with a '98-up harness)

Cosmetically:
-fog lights get cracked from road debris
-pwr. window switch plate clip loosens then the whole assembly pops out of its hole in the door handle
-center console lid loosens or breaks
-cheap Chevy leather cracks
-seatbelt guide on seats break
-rubber molding on rear hatch glass tends to shrink and come apart from age

Mechanically, in addition to what ZDriver stated:
-rear main seal will leak
-intake manifold gasket will leak oil at rear
-differential will make whining noises if it's had a rough life
-check for leaks around the differential housing
-throwout bearing tends to be noisier on older cars
-I believe the early LS1 cars ('98-up) had a recall for their oil pumps failing