I've had a few problems with my Sainsonic Arduino Mega 2560 board with the 3.2" Touch screen. Most of them are related to the undersized voltage regulator on it once it had got a bit hot a few times for too long.
By using my Freetronics Eleven boards regulator bridging to the Sainsonic board I have completely eliminated the glitched pixels while drawing, which once I had a big program running on the unit would become apparent.
The Sainsmart Mega Board below can be seen with the smaller voltage regulator. You should also notice that it still retains reference layout for the pin holes around the regulator for convection and cooling, despite having a different size and location regulator...
You get what you pay for people! If you have a Sainsonic arduino mega product and have obvious screen draw errors, or a white screen I'd recommend upgrading to an external regulator and you probably have a much better experience with your unit.