The tenant believes moisture is getting in from under the unit, however, we believe this is from their lifestyle. 

Try to get a free inspection from mold assessors, structure companies, crawl space encapsulators, etc. paying particular attention to the wood moisture content under there.

We also have tenants sign off on this form:DISCLOSURE OF INFORMATION ON MOLD AND MOISTURE HAZARDS(Addendum to Rental Agreement)The Rental Agreement dated _________ between ____________________________ (Landlord) and _____________________________________________ (Tenant), of real property located at __________________________________________________, is hereby amended in include the following terms and conditions: “Disclosure of Information on Mold and Moisture Hazards.”

If there are water marks and evidence of continuing water penetration, the first order of business is to stop the leak. 

Hunter Byler just make sure it was done properly and that there are no signs of mold from the moisture.

They stayed warm due to generating lots of heat internally and only heating the portions of the house being used {i.e. you would not heat the dining room or salon during the night}.With older properties we usually lay-out a plan to improve the building envelope first through air sealing (getting rid of drafts and convection within the wall cavities) and, where possible, insulation {not always straight forward ... many old brick buildings have limited insulation options due to the brick requiring heat transfer from inside to drive moisture from the brick}.Around here it is not uncommon to find an old mansion converted to multiple units - or the occasional purpose-built multi-unit - where the operating costs are 70 - 80% of the revenue and heating comprises 20 - 25% of the operating costs.  

The siding is asbestos siding (they painted or "sealed" it), there is moisture and some water damage in the crawl space, and an old termite infestation.

The pic on the left appears to be the result of moisture infiltration.

It's slowly but surely being penetrated by more & more out of the area investors because of the market prices. 

It's still a very hard market to penetrate as entry level.