Make sure that the source of the moisture is also remedied-ie proper ventilation in the attic and basement.

There are also stucco inspectors who will drill a hole in each windowsill and do a moisture test.

I had a plumber look at it and cleaned/re-caulked where the foam gasket completely deteriorated and replaced the broken shower handle for 320.Then the restoration guy came and did not detect any moisture in the garage wall or upstairs bathroom. 

@Joey Allison Mold is fairly common in Arizona, once moisture is introduced it can take off pretty quick.Mold is also very treatable in most cases.

@John Underwood You could get a moisture reading in your crawl space to see if you have a problem that needs to be addressed.You might need a moisture barrier if you don't have one.

Getting rid of it is fairly easy:  stop the moisture intrusion including condensation and clean with bleach.

However from that list - the most concerning items are associated to appearance of mold (laundry wall room/ behind hall bath toilet) and identification of active moisture (laundry room ceiling / active moisture intrusion at lower wall of converted car port) in a few locations.

Just about any home built since about 1960/70 is designed to have functioning air circulation systems, and without circulating the air you are going to have mold, moisture, heat soak and other issues.

It compacts down and becomes water-impervious as opposed to dirt which can absorb moisture and could continue to cause moisture.

Roaches may like the moisture of a bathroom but they still need to eat.