Two questions, first, is the moisture evident only when the screen is blank (black) then is no longer easily seen when the screen is active? Second, when the moisture is evident, If you remove the phone from the case is there definitely moisture droplets on one or both surfaces? If the answer to both of the above is no then I would not worry about it. I see something similar on my phone occasionally depending on the lighting in the area. I'm not sure about the scientific term for it but it has something to do with the way light passes through the plastic screen protector of the case and the fact that it is so close to the phone's screen. Something about refractive interference. If the answer to the second question is yes then its time to watch how the phone is being used as it is being exposed to moisture somehow.
As far as washing the case goes, I do wash then rinse mine every couple of months or so. When done I wipe it off as best I can then let it air dry overnight before putting the phone back into it.