Well, being an older car in Ohio... rust.
I don't have experience with the TT specifically but have experience with VW's in Minnesota. You should take a close look at any wear items that tend to go out around the 80k-100k mark that may not have been replaced and are somehow still working. Like the water pump, timing belt, clutch (if it's a manual), etc.
Also... the electronics. Older VAG cars can go a bit haywire. Make sure you get it scanned with a proper VW tool and see what errors and codes are stored. Make sure no lights are on the dash, too. Verify consistent operation of as many electrical functions as you can, including lights, power windows, etc. Check the HVAC and make sure heating and cooling is working properly (another common problem is the engine thermostat can get stuck open and you will not get hot air in the winter).
And as with any used car, try to figure out if it has been cared for or abused. In my limited experience German cars NEED their regular maintenance done and always to spec. Put the approved oil in. Take it to mechanics that are trained to work on that car. Regular oil and fluid changes. If the previous owner's were not diligent it may have some problems.
Not trying to scare you away, just use common sense and check it over good and take your time. The TT is a very cool car. Good luck.
