Very little, I have had the car for around a year and so far I have had no problems at all with it.
Apart from the unavoidable stone chips around the back wheels arches.
I have heard a lot of rumours of leaking roofs, but myself and two other friends who own similar cars have never experienced any problems with water leaks, even under the heaviest downpour.
Performance is very good, not awesome but bloody quick, BMW quote 0-60 in 6.9 secs but on a dry day, 6.4 seconds is easily achievable.
Handling is corking, traction control gives you the extra confidence in the wet or in Winter conditions that other rear wheeled drive cars lack, but in the Summer by pressing one little button it's rear end out fun, quite controllable and with the hood down an absolute scream.
At my time of buying I test drove rival cars for two days each and the 2.8 Z3 was the best for handling, performance and all round fun.
But just a word of warning, take a large steepish slope, add snow and slush and then take 196bhp driven through the back wheels and the result, not a lot of weight over the back wheels will leave you stranded and unable to get traction. Rather embarrasing!
But that's the price you pay for 50/50 weight distribution.
All in all another excellent roadster from those clever little German bods.