I need a few tips on what to look out for in shopping for this car. Information on any known mechanical problems, shortcomings, or maintenance issues would be appreciated. Thanks very much.

 

Look at the top of this subforum - sticky post about the TT and the 1.8T will fill you in.

 

i wouldnt desperately look for one unless you are looking for a project and just settle for the cheapest.
theres lots of info here , ttforum.uk, and on vortex.
i would make sure timing belt and everything that goes with it is done , look at the seats, glovebox, lcd display, bushings on sway bar make a lot of noise unless you grease them and replace them. just google it audi tt buying guide and let us know what you find.