You can take a black light and see the extent of the urine damage on floors,walls,ceiling,etc.If the animals have been peeing in the corners it can soak the wood and floors.You want to make sure you really get rid of the smell before selling.

Earlier this month, my tenant uncovered water damage along the baseboards and lower walls of the master bedroom.

I would just let it go unless there is property damage concern.  

This minor leak could have caused an unbelievable amount of damage that's not obvious at the moment.

They still need to keep it under control and make sure it doesn't damage anything or bother people. 

They are both tied to the lease and both responsible for all damages.

I imagine pros would be having some sort of proof that the tenant damaged the place under their watch and having some sort of recourse for it.

I might get an inspection and give myself an out for bad cast iron pipes or other significant structural damage.

On the day of cleaning, my cleaner sends me texts and pictures of all the things that may be dirty or damaged. 

He's mostly late in paying the rent, emotionally unstable and troubling the neighbors, has caused damage in the property, etc.