I think you have two different things going on. The light colored spots look a lot like thrips to me.
The little black specks look like a mold of some type like others have said. It kind of reminds me of black suety mold, like what grows on the Honeydew that aphids excrete, not sure though. I have had Black Suety mold from watering with way to much molasses, as well as from aphids, or it could be a different type of mold.
Check out the tutorials on: Thrips,and PM for sure. Look at the one on mites to, just to be on the safe side, but I don't think it is. Drying out the surface of the soil, lowering humidity, and more air flow should help a lot with any Fungal infection.