Mine is coming upto 5 years old and has done just shy of 60K.
Issues I've had:-
Rear left brake light failure (sorted itself and never played up again in the years since).
Rear right suspension damper seized - I drive with the Magni ride turned switched to hard as I find the ride and steering just to loose when set to soft so it might have had something to do with that - 50/50 as the car was out of warranty.
Haldex hydraulic pump failure (replaced under warranty - otherwise a ~£1500 bill I believe).
Rear centre brake LED cluster had several failed LEDs though I believe this was caused during a rear end shunt and it was replaced as part of that repair. I've seen other TTs with random LEDs not lit on the road. It's something like £200 to replace if I remember correctly.
Drivers door dropped a 2-3mm - done this a couple of times.
Paint (Daytona Grey) has started to bubble on both doors in a few places - this seems to be a general Audi issue and is apparently contamination under the paint rather than a corrosion issue but I'm going to see if Audi will cover it when I'm in for an MOT in a couple of weeks.
BOSE Amp indicated a failure when in for a service - I was quoted £400 to replace it if I remember correctly, even though it was working fine - no further action was taken and it's still working fine 4 years later.
The bloody wheels are prone to collecting grit and other small road debris in the corners of the spokes unbalancing the wheels which then makes for rough driving and oddly rough gear changes. Keeping the wheels clean resolves it
The auto dimming on the wing mirrors seems to have failed on the passenger side, need to investigate this more.
Other issues in general I'm aware of but I've not experienced:-
Stronic boxes are known to be a concern on the MkII TTS with high failure rates. Something like £1500 to replace at the dealer I believe. It's thought to be caused by low speed driving (<5mph, so traffic jam sort of stuff) cooking the boxes
Window regulators, similar to the A5 are prone to failure due to the shunt up and down everytime you open/close the doors.
Saggy bottomed seats
My timing belt is due for replacement, been quoted £550 at the dealer I think it was, including replacement of the water pump and also free MOTs for the life of the car.