One problem related to transmission failure has been reported for the 2004 Audi TT.
Audi Tt dsg transmission fails and the car loses all ability to accelerate. This has happened in traffic. All transmission display light flash rapidly (prdns) while the car will not move without turning off the ignition & restarting the engine. Problem has occurred a couple of years ago and now twice in 1 week. Appears to be a safety hazard as failure can occur in traffic & vehicle is without power unless ignition is turned off and then on again. Google search reveals a great number of these incidents. While Audi has issued extended guarantees on newer Audi Tts and some vw products with this transmission, they have apparently not addressed the issue for owners of older Tts with dsg transmission like myself. Have 2 videos showing flashing display.