Red Eared Sliders and other turtles can develop fuzzy gray and white patches that are fungal growths. One of the major causes of this is poor water quality and a improper basking area. Make sure you have a good full spectrum or UVB Light bulb and heat lamp that gives off some good heat. Turtles need this for the prevention of fungal infections. Another important thing is a basking area. Your Red Eared Slider Will need some sort of land mass to completely dry itself to prevent shell problems and respiratory infections.
ACRIFLAVAN, is available at most pet stores and will often eradicate fungal infections when it's added to water. I also recommend Hagen Sulfa bath and Betadine. If you choose to use Betadine, apply a small amount to a toothbrush and scrub the turtles shell. Once the Betadine is covering the infected areas, let it stay on in a dry area for 20 minutes. Repeat this process twice daily for 2 weeks. Make sure you do not get it in the turtles eye's. If this happens, please rinse the res ASAP.