One idea I'm toying with right now is to ask the tenant to retain her own pest control services and to send me the bill if they find evidence of a rodent problem, but I'm not sure if that's legally defensible.  

And if you don't find out until they move out, and their deposit isn't enough to fix the ruined floors...I think addenda, even if they're just informative, regarding mold and bedbugs and pest control, etc., are a good idea.  

Reasonable cleaning costs would include the cost of such things as eliminating flea infestations left by the tenant's animals, cleaning the oven, removing decals from walls, removing mildew in bathrooms, defrosting the refrigerator, or washing the kitchen floor.

Make sure your tenants understand their rights and obligations as stipulated on the contract.Each of my rental units has fridge magnets with the contact information of my plumber, pest control guy, and electrician on it for the tenants to contact directly.

Other than that, I wouldn't worry about their housekeeping unless it is causing problems- mold or pests for example.  

Anyways it's a duplex and the apartment is infested with roaches and every other insect there is.

That's my take on the drama stuff.And otherwise, it's easy peasy dealing with pest control or inspections, etc., when you've only got one building.  

People don't get multi-million dollar awards because of no-fault accidents.So, limit your liability by removing problems you could get sued for - make sure the electrical is to code, and there are fire extinguishers, provide outside lighting if it's a bad neighborhood, take care of pest control, make sure the roof won't collapse, that stairs are in good order, that there are no swimming pools kids can get into.I just can't think of any "terrible injury" that could have been caused by you, if you just take care of the property.And, of course, get a reasonable amount of insurance to cover you for any accidents that may happen, that a tenant may file a claim against you for.But, to put things into perspective - I managed 25 units for 8 years as a resident manager.  

You can require ALL tenants to exercise responsible animal ownership, protect the property, minimize chance of harm to other people, and maintain acceptable noise levels that do not interfere with neighbors' enjoyment of their own property.A well-written animal clause will require the tenant to:Provide proof of current shots, if applicableProvide proof of flea control medication, if applicableDisclose the name and contact information of the veterinarian caring for the animal, if applicable (hamsters, for example, probably do not have veterinarians)Keep dogs in a crate or on a leash at all times when outside the dwellingUse a pooper-scooper, whether on the leased premises or another's propertyVary locations of dog urination, so as not to burn shrubs or lawnEmpty cat litter boxes daily into outside receptaclesControl  excessive barking that disturbs the neighborsAllow monthly inspections for pet damageImmediately clean any pet discharges and immediately report any damageAssist with Twice monthly HVAC filter changes for long-haired animalsKeep pet food supplies in pest-proof containersI think that if you approach the problem in this manner, you will be more comfortable complying with Fair Housing laws.

pest control!!