If it is from moisture and its no where else except where they have the portable AC, then it is their responsibility.

So, I have a somewhat working knowledge of physical plant issues (sagging roofline, foundation issues, vapor and moisture problems, etc.)

Redguard acts as a moisture resistant barrier on top of your cement board.

The first thing you do is check the moisture outside, get a reading and then check the moisture inside, but then you still need to find where the moisture is coming from and most contractors today use an infrared moisture tester that shows an image of where the moisture is coming from.

Moisture is not good but if there’s no damage/corrosion of the live equipment then it’s not necessary yet and your better off dealing with the source of the moisture.

During the inspection process of our 2 bed 2 bath condo in Inglewood, we noticed some discoloration and moisture marks in the top corner of the master bedroom closet.

Now, I don't know how to insulate the roof to avoid condensation and moisture issues.

Some of the failure mechanisms are rusted connection hardware, crack treads, spalling from freeze-thaw cycle, and decay from moisture.  

If you are waiving, you need to determine the source of the water moisture causing the mold and the extent of the mold. sometimes, mold can grow in non-visible areas and can be worse than visual assessment. 

It's all particleboard but what they use tends to be thicker than Lowe's, reinforced better at the edges and the countertops have a better laminate round-over wrap to keep the moisture off the particleboard on the edges.