Unfortunately, simply urinating on the property corners does not meet the notoriety test:)  To get the idea of fencing, you might pound survey stakes in the ground every 12 or 15 feet along the road frontage, and for maybe 50 feet down the sides.

For mice you can usually treat the urine stains ... we often use just hydrogen peroxide or, if it is really bad, one of the enzime products specifically for animal urine.  

Make sure before they move in there is no urine or pet stains in the apt and state that the unit they are about to move into is indeed free of it (put this in all of your leases) also keep an eye out for damage to door jambs and the bottom of the doorsService animals do have documentation and you could ask for it

For example, With the smoke and cat urine, I would need to pull up all the carpet, remove the staples, clean and seal with Kilz, and repaint and lay new flooring.

You may also need to remove the lower portion of drywall to insure you get rid of all the urine.

If there is dog urine, don't be surprised if it seeped through the carpeting, to the carpet pad, or even to the floor underneath.

I sometimes find it is actually the walls that harbor the nebulous sort of hard to spot animal smells (not urine per se, but just musty).Try a sponge mop dipped into warm water and TSP (just damp) and clean the walls, then rinse with clean water using the same well rinsed damp mop.

There isn't one person with a pet that will tell you the pet isn't perfect.. yet check here on BP and find out how much damage urine, chewing, yard damage, nuisance barking, pets cause let alone injury from bites and attacks. 

Dogs and cats urinated all over the carpets and the house now has a very strong ammonia smell.

Think it's a homerun but it's infested with cat urine and the cats are still living there.