This effectively mitigates the need for a large liability limit on the property insurance so long as you are doing a good job with property upkeep and your other responsibilities.

This is only possible if you buy right.To mitigate the issue of not being able to refinance if you can't sell(extremely low possibility), get pre approved with a lender.

In most scenarios, military towns are cashflow markets therefore, it's easy to charge a bit more for rent (depending on the Soldiers BAH) and build reserves that mitigate the risk of high turnover.  

There don’t seem to be any cracks in the basement floor/foundation, but there were some mold spots that would need to be mitigated which also supports that it could be a water issue.Any idea what a fix would cost?

There are ways to mitigate the issue.

Asbestos mitigation,Updated bathrooms and laundry, new flooring, paint, doors/trim, and windows.

I´ve seen properties where the foundation, waterproofing, mold mitigation,  and rotting sewer pipes alone are well over 100k.

It's those maniacs that buy homes cash via quit claim deed off of craigslist that really get screwed.Make sure your property manager is a licensed real estate brokerage.Google Clayton Morris and/or Morris Invest for a cautionary tale of what not to do when buying turnkey real estateUnderstand you can not eliminate all risk, only mitigate it.

However, these costs will hopefully be mitigated some by the income I receive from my tenants.

Legally I don't think there is anything you could do as of now to mitigate the issue.