Honestly if I were a landlord I'd require topical flea preventative from the vet, not the grocery store stuff, and be able to provide proof of purchasing it. Course that's not to say the people will actually use it though.

A house/apt. infested with fleas can get out of hand very quickly, and cost a ton in hiring an exterminator, replacing carpeting, and possibly spreading the fleas to other appt's in the building adding even more to the cost.

Other than that the only other thing I can think of would be monthly unscheduled inspections. If they schedule a day it would be easy for someone to hide signs that they were a bad pet owner or not following the rules. I figure if after a year of unscheduled inspections and if everything is ok, then probably go to only inspecting ever other month, then gradually stretch that out perhaps. JMHO

Biggest issue is that not all landlords love pets, and not all pet owners take proper care of pets, sad but true fact. The strictest landlord in the world can still have money lost by a bad pet owner, and a good pet owner can still be burned because of other bad pet owners that have jaded the landlords. I don't know that there is a win-win scenario here. I think you covered the basics though with background checks, vet referalls, etc. Good luck with your project.