I have a basement that has a very low rate of moisture influx thru the cement.

If the inspections come back as lots of structural and moisture damage I will raise my bid to 500 after (PITI/PM) per house or back out. 

The base plate 2x4 is 40% water ( I have a moisture meter).

Here are somethings I have dealt with on mine:Sealing baesment walls from moisture; jacking up original porch to keep it from pulling away from building and causing damage, jacking up floor supports that were sagging, and converting fuse boxes to breaker boxes; tenants installing window a/c units then damaging the window frames with water rot. 

I have used this flooring in basements that get moisture and its great. 

I would think having a bathroom vent going into the roof would cause moisture, which could result in even more problems. 

Find the source of the moisture.

The biggest problems I've seen with hoarding houses have been related to moisture damage and mold.

The mold contractor recommends taking care of the moisture/dampness issue first, OR just get a dehumidifier that drains into the sump pump because it is very normal for new jersey basements to have moisture in the basement.For waterproofing: from speaking to different contractors, I was told my options are to install a french drain (best quote was $4,800) or another option was to escavate the exterior of the foundation to waterproof it from the outside, and re-grade the gravel on the exterior of the foundation (VERY expensive >$10k), or the third option is to just do the dehumidifier and drain it into the sump pump as the mold contractor suggested.The buyers still want the house, but I don't want to spend a ton just to finish this out. 

As far as moisture, I look on the wood for white residue as a sign for concern but I don't see anything like that in your pics.