I am no expery on the tt but overall they are suppose to be pretty reliable.
If its a long drive check the engine oil as some are known to use oil.
Pre 2010/11 are cambelts then the engines wer revised with a chain and around 10bhp more and suppose to be better mpg. I would of liked this engine myself but spending cash i had a limit. Not 100% when they including the led drl type front lights could be the same.
Common things are saggy leather seats, noisy/failing window regulators, knocking steering racks & poor connections to rear lights, making them dim.
Otherwise normal things to check like the turbo is kicking in nice and strong and should pull from low down. No apparent turbo smoke coming from the pipes.
if it has the bose sound system make sure it works perfectly as the amps are expensive and known for going as they are located in the rear passenger panel and can get damp and moisture damaging it. So if you have the bose and it works get some sealent around it like a wax/sealent ect
The tts is the same engine obviously beefed up not sure if anything extra to look for .
I would like to race a tts now mine is mapped. I reckon mine is around the 230bhp as i had no upgrades just a remap and the tts being 4wd will sap some power so would like to see the difference. And yes i know a tts remaped would leave me for dust.
hope i helped a little