The accelerator response. Seemed a bit random. I could definitely detect turbo lag but it seemed more than that. One minute it was very responsive, the next I pushed on the accelerator and nothing seemed to happen.
I think what you were experiencing was how the DSG gearbox actually works, nothing more than that. The DSG box takes a bit of time to get used too, and you have to game/know it to get the best from it if you aren't in manual mode. I first had DSG in an RS4 (albeit Audi call it S-Tronic) and I was initially very disappointed as I expected the shifts to be instantaneous regardless of what the engine was doing, but once you live with DSG and understand how it works and what it needs, it all becomes clear.
For example, if you are in 'auto', revs dropping down slowly and you're off the accelerator, then the gearbox is ready with the next gear it 'thinks' you'll need. If you suddenly stamp on the accelerator, it'll hesitate, select the gear you now actually need, and off you go. All this will take a bit of time, and cause momentary hesitation. DSG can do this quicker than any other 'Auto' box, but it can't defy the laws of physics. On top of this, depending on which mode (Eco, Comfort, Normal or Sport) you have the car in will further increase/decrease the hesitation.
If you're wanting the ultimate gear shifts from a GTI (or any performance DSG equipped car), then it's best in 'manua'l mode, you are in control of the shifts and gears, and it brings your driving ability/connection with the car.