I also run an ionizer to get rid of any lingering chemical odors.  

Some tenants will keep it really cold and then create lots of moisture through showers with lots of company, cooking, plants etc.Did you ever notice any odors before you rented to them?

There might be the build up of body odor in the bedding. 

Looks like the only "urgent" thing, if we let tenant go, is to get rid of the smoke odor.

If you are going to paint anyway, prime it with a Killz odor blocker primer first.  

If it is a small area cut out the pee area, bleach the subfloor and paint Killz odor-blocking primer on it. 

Additionally it doesn't have the odor for guests and is supposed to be better for skin (perhaps a slightly better pool user experience). 

You can require that no "offensive" odors be detectable in common areas or outside of the residence, and that proper sanitary conditions are maintained.

You can also require the animal to be on a leash or in a carrier in common areas, unless that inhibits the task or service the animal provides; handlers must clean up after the animal on the property; no offensive odors can emanate from the residence.

If recently there is still the potential issue with odor if it has not been sealed property.