The engines are fairly bullet-proof, and problems are extremely rare. The only issues I am aware of are turbo wastgate actuators, which can rust or seize, and diverter valves failing. If you check the boost when driving it should reach 0.6-0.7 bar at wide open throttle (standard car). Any less could be a problem, any more is a sign it has been remapped. The actuators are about £300 each, and the DVs about £60. (parts prices only)
Other than that, they suffer from the same troubles as all other 996's - aircon rads, etc. They also suffer from saggy rear suspension due to the extra weight, but this can be sorted either by new springs at £150 a pair, or a trip to Centre Gravity which I would highly recommend.
Also, don't be alarmed by a puff of smoke at start-up. They tend to do this a lot more frequently than the Carrera.
HTH