I purchased a moisture meter and checked the drywall and baseboards in several spots.

Kilz is good stuff, but won't necessary cure mold.Do you know how the moisture got into the closet?

What we discovered was that the house has a floating slab so there is a small channel around the whole thing which would normally catch any moisture and either route it to the floor drain or let it evaporate but in this case was used to feed moisture directly to the finished surfaces.

Basement - a couple of things 1- is not completely dry has humidifier that I turn on now and again to lower moisture as floors (concrete) can get some water in it. is this a problem for a rental?

After the brush has been mostly clean you can then gently ham it into the sink bottom to remove the last little bit.

Evidence of moisture on some of the walls including under a window well.

Sherwin Williams is my employer.I don't mind the advice to clean the walls just be mindful of how much moisture you are putting into the walls, especially if you are planning to use an oil based primer.

good mold or bad mold is not the problem whether or not tenants will get sick in the future or anyone for that matter it's obviously serious but if you have mold or can smell mold what you really have is a moisture problem or a water problem and whether or not the mold will kill you or not the moisture will kill the house you need to find the water you cant stop all the mold until you take away the water .

Homes in our area were dried out, cleaned, and moisture levels documented. 

The company inspector brought her moisture indicator to run over walls and ceiling, and did not detect any moisture after 2 days of the heater.After the roofer removes those damaged panels, will mold in the insulation--or ceiling sheetrock or joists be a problem?