I bought a 2002 Z3 2.2 Sport back in the summer, never having had any BMW before. I had to change the rear bushes on the front control arms to stop it from wandering all over the road. A cheap fix that made a terrific difference. The other thing is that I have two different brands of tyres on the front wheels and that leads to a small degree of "tram-lining", but the tyres have too much tread to throw away so I'll live with it for now. The rear tyres are a different size else I would swap them over.
Other than that, the car is super. The engine at 78,000 miles is so smooth it's dead easy to hit the rev limiter when pushing on a bit. Unlike my MGB V8, the Z3 has to be revved to get it to perform which took some acclimatising for me. The old Rover V8 just pulls like a steam engine from 500 rpm, and you never need to exceed 4000 rpm. The Zed is very different and doesn't feel very quick if you change up early. Let it rev and its lovely.
Mine shows little sign of corrosion, just some stone chipping on the leading edge of the sills, which I will sort out soon. It came with brand new brake discs and pads all round and a new soft top, so I'm well pleased. There are plenty out there so find a good one, even if means travelling. I bought mine 220 miles away from home.