Quattro is almost as synonymous with Audi as electrical problems are. That said, there are a few things to know about the TT's Quattro system.
The TT's engine is mounted transverse (sideways) as opposed to longitudinal (straight). Therefore, it must use a different AWD system than the longitudinal engined cars (The A4, S5, etc...pretty much any Audi sedan). The TT's Quattro system is referred to as the Haldex system, named after the Swedish company that manufactures the differential used in it. Haldex also manufactures the AWD system used in the Veyron. The longitudinal version of Quattro is called TorSen, short for "torque sensing."
TorSen, first of all, differs mainly in that it maintains a constant 50/50 power split front and back. Upon traction loss, it uses EDL (electronic differential lock) to transfer power appropriately to regain control. This makes for a generally more neutral feel to the car.
Haldex, on the other hand, is heavily FWD biased. The system uses the standard FWD transmission with a Haldex clutch in the rear to engage the rear wheels when necessary. Due to the drivetrain design, power passes through the front differential first and then goes to the rear, therefore no more than 50% of power can transfer to the rear under any circumstances. Haldex is almost constantly transferring some power to the rear, however the FWD bias is people's main criticism of Haldex. The ability to disengage the rear wheels, however, results in less drivetrain loss and improved gas mileage.
Fortunately, for about $700 an aftermarket Haldex controller can be bought to increases the power shift to the rear. The Haldex "Blue" controller shifts 50% of power to the rear immediately, causing a more neutral feel and more inclination to oversteer. The Haldex "Orange" controller is the same as the blue, except it doesn't disengage the rear wheels under braking. The makers of the "Orange" claim that this allows the car to brake with the drivetrain, which is how the original Quattros managed to outbrake the competition. This has proven dangerous on the street though, and for any street application, the Blue is the better choice.