The first time we did it, we had the other sides of the shower wall studs all exposed, ran the shower for several hours to watch for any signs of moisture, and saw nothing. 

Install new Housewrap weather and moisture barrier.

How's the roof, foundation, moisture and neighborhood?  

For moisture... bring with you a moisture meter.

The moisture meter was off the scale in this area and the ammonia odor made your eyes water.   

I did notice the windows in the guest house have broken seals (dual pane w/ moisture inside) - did not notice this on the main house.

I have had a tarp put in place to stop the moisture from getting in.  

I would suggest a newer build [1998-up] like a subdivision "vinyl village" home to purchase.These will cost a little more than an older home with the same rent but are much newer, typically on a slab [no moisture issues to deal with] and are easy to rent and/or sell in the future.One downside of this type of home is that most good markets [Indianapolis included] have been invaded by the Wall Street Hedge Funds and they have or are buying up this product at record rates.

We would have noticed how bad the moisture damage was right from the get-go.

This is a problem created by them so they are responsible for repairing it.Mold requires moisture and a food source (dust).