Extra moisture resistance, more flexible, or special in some other way?

Mold is caused by moisture, so if you get rid of the moisture your problem is solved.  

The walls will be dense-packed with cellulose, which is a great buffer for moisture, but thicker walls can be slower to dry out than normal walls. 

Hi BP,I am new to this form so please be gentle!

Exterior measures were taken about 20 years ago and the moisture issue comes and goes.. literally years can occur between.

Letting someone down gently is an art.  

Below are some generalizations about ongoing maintenance costs: Older properties require more maintenance than newer properties.Composition roofs require more maintenance than tile roofs.Properties in climates with hard freezes require more maintenance than properties in milder climates.Properties in locations with a lot of moisture require more maintenance than properties in dryer climates.Wood siding requires more maintenance than aluminum or stucco siding.Properties with lush vegetation require more maintenance than properties with little or no vegetation.Below is a typical Las Vegas single family class A home.In summary, I believe Las Vegas is not only a good place to invest today, it has a high probability of continuing to be a good investment location into the foreseeable future.

Recommend sloping grading away from home 1" per foot to avoid grading erosion, foundation seepage and possible foundation movement (85-90% of all foundation moisture problems can be avoided with proper grading and downspout extensions).

This is my first time... please be gentle.

I believe you usually staple moisture barrier to the studs before the cement board and tile.