The Triplex needed a new roof, moisture in the foundation, Caribbean termites and damage from them.

So, there were issues that we noticed, like moisture underneath the house.

I just got the home inspection report- the roof is thrashed and there is significant moisture damage throughout the house.

You should use a moisture tester on all the lumber and make sure it is dry before drywalling. 

I recently had a tenant move out. He claims that in a spare bedroom, which was hidden by a bed, when he moved the bed out he discovered an extremely raised section of the hardwood floors. The "peak" of the raised sect...

I was thinking the same thing - seems like the moisture is coming from the cooking itself and not exactly the fuel source.

Crawlspaces/subfloors are particularly bad about humidity and moisture issues. 

My GC primed and painted over them a few times thinking they were just old, stubborn stains that needed extra product, but they kept coming back after each rainfall.I hired a water intrusion detection company to help me pinpoint the problem - they said the new roof seemed solid and that based on infrared and temperature readings, the moisture is coming in from the partition walls.

Furthermore, bad installation of siding seems to be more common than not and results in damage to the structure over time from water and moisture infiltration. the best part is, you don't know it until it's beyond a simple fix because all that lovely plastic siding is hiding telltale indications of problems.

If they feel like their is mold although someone has already inspected for that ... you can get one of those water scanner things (sorry I have no clue what it is called) but it essentially checks for moisture (it shows certain color based on the moisture) also I would remove the base boards and cut about a foot of the dry wall to see if that is wet.