We have an '01 TT quattro coupe and it has been great. We had some trouble with the sending units in the fuel tank but nothing else. It is mainly driven by my wife as a daily driver and she is not an aggressive driver. Nonetheless, the car has been great.
However, from reading, I think if I were looking at a car of that age now, I think you want to find out about the timing belt/chain. I hear they can cause some serious damage if they break and while they aren't cheap to replace the money is well spent especially if you tend to utilize the car's performance abilities....if you follow me.
Other than that, I haven't heard of much in the way of chronic problems with the cars.
Good luck with your search.