I think ub7rm has stated most of the usual reported faults above.
If you're completely new to the GTi world, I would suggest the following additional checks to ub7rm's
1. Check the PDI dealer and stamp in the Service Book to see if the car was UK supplied or not.
2. Check the alloys are genuine VW ones. They should have "VW" and "BBS 349" or something similar stamped on the inside of the rim.
3. Check the boot for a spacesaver spare wheel (UK spec) and any signs of leaking - the seals have been known to fail and the boot well get wet.
4. Check the upper brake light strip in the rear spoiler for bad condensation or bulb failure (another common fault).
5. Check the fit of the front doors (some early models suffered from the door dropping slightly and excessive wind noise)
6. Check the DSG is smooth at low speeds, when fully warmed up and setting off on an incline. If there is a small delay followed by a lurch forward I would get the DSG Mechatronics looked at before buying. There is a known problem with a batch of these but I think your car is older than this, so you should be OK

.
Good luck with your purchase .. hope all goes well .. sounds a nice car
