For example, one had a missing ceiling panel with mold and an unusually damp basement (although containing a sump pump).

A wet/damp crawl space can add another $3-7K.

But that was before the current model just being a drop off and pickup point and sending the clothes out for cleaning.

Clothing? 

So I can detect cigarette, cigar, and pot on clothing, in cars, and in apartments and houses.I bought cling stickers for the windows near the front doors that say "Smoke Free Premises - Thank you for not smoking."

It's common on the floor joists with a damp basement in Indiana. 

If the floor is damp do nothing.

He will probably supply $200 of material in drop cloth, tape etc even if you buy material.

A lot of times you end up finding cloth wiring or you have to pull extra circuits to the kitchens and baths because you opened up the walls. 

Gas, food, clothing, utilities, all cost the same whether you are rent subsidized or not, so there must be other verifiable resources to readily pay for those items.