The house sustained some damage that is not an insurable loss.

I have had people pay for a couple of small things that were damaged. 

My concern is that someone is going to damage something and not take responsibility for it.

This is only going to get worse and cause more damage. 

A rotten flange can cause raw sewage to get into the basement, water damage and what not, but it should have zero effect on the water bill.

re: moisture damage. were the pipes sweating that much to cause such extensive damage or what is the alleged cause of "moisture" from the ductwork?

It's a smaller house so the premium for replacement cost over 10 years vs the actual cost of replacement in the event of serious damage might break even. 

The other part I didn't see mentioned is that you should charge the tenant 100% of this service cost for the repair assuming your lease makes mention of tenant caused damages being their responsibility.

Such as smoking or causing damage to the hotel room?

This is my old insurance hat coming out, but garage parking also opens the door to potential damage with mirrors clipping the side walls, issues with the garage door getting hit, etc.