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With older (and many not so old) buildings, it's almost impossible to prevent their entry, but it is possible to make the building less attractive of a place to stay.Mice breed quickly, so ultimately they become the property owner's problem regardless of how they entered and whether the tenant laid out a buffet enticing them to stay.  

Turn into affordable living space a basement space that is deteriorating and empty, which is attracting squatters and/or thefts near the building disturbing my current tenants and the neighboring properties).

The apartments are near a university however we don't tend to attract off campus students.I'll consider the 50% of first months rent for attraction.

I seem to always attract a large, qualified pool of tenants.All the tenants I have had, had medium to large breed dogs and they have all told me how grateful they were to find a place that allowed their pet(s).

@Zamir Kazi  A cash offer is a very attractive offer.  

No one calls their property manager out of the blue to compliment them on running a safe, clean, attractive building.

I rarely have cash in my wallet, let alone pay any bills that way.

If they are sugar ants finding their way to the kitchen, remove all food sources that are attractive to them, find their route of travel and set some bait traps where they will enter the trap gather some bait and bring it back to the colony.

There is something about doors that Tenants seem to be attracted to, like little puppies loving to chew on things.