Since home inspections/termite & moisture reports are typically for informational purposes only.

The ceiling is falling in in one spot and moisture seems to have create a mold problem, locally around the leak.

The current set-up has no vent for the dryer so it is venting all that moisture into the basement. 

In smaller bathrooms I have been pulling out the small vanities (they're usually pressboard) and putting in a pedestal sink which is impervious to moisture. 

The one item that really frustrates me is when they call for elimination of moisture in a basement--water proofing. 

Think about it.... the people who show properties to tenants and do walkthroughs upon move outs may not be maintenance inclined people who are going to look for cracking caulk in moisture areas or other things of that nature.

For cold zones behind walls and not proper insulated you can use a thermal image reader.For leaks you use a moisture meter.Active leaks will register above the required safe threshold.As you get closer to the leak the moisture reading will be higher.How do you know the GC did everything above board??

After the tenants left, I spread some new seed over the bare ground, covered it with a layer of straw to hold moisture and the lawn quickly grew back.As to training your tenant, communicating your concern is the place to start.  

But first priority is wet stuff out, dehumidifiers in and no work done until moisture levels in floors and studs are within normal to put new  sheet rock and flooring in.I've had some experience in storm related work with tenants, leaks, minor flooding.

I have had some moisture issues in that unit since then, but it didn’t seem to effect the walls.