Two primary issues have caused the most problems: Transmission, and the "check engine" light.
The Transmission will sometimes shift harshly between gears while in Automatic mode- I have taken the car in three times for this issue, and have been told this is only a computer code problem. The Transmission computer is cleared, reprogrammed, and the transmission runs smoothly again.
The "Check Engine" light (CEL) has been more insidious. About ten months ago the light started coming on- I took the car into the Hyundai dealership, as I didn't want to continue driving the car under warranty. No cause of the light was ever detected. Since then, I have taken the car to three dealerships in two countries (for a total of ten visits) and the problem still has not been rectified. On the other hand, there have been no technical problems with the car, other than the light coming on. The local dealership has informed me that if the car starts demonstrating physical problems to bring it in- otherwise, ignore the CEL.