Even though we know why there are lawyers and how they operate and that agreements really dont mean anythings, now the question, does anyone have a waiver that they have tenants sign for such potential risk that reflects that tenant will pay all legal fee's/court cost, etc.... if property owner is pulled into any lawsuit as an outcome of their pet hurting someone?

Remember the entire purpose of screening is to find reasons to eliminate applicants.Look harder, consider why some are free and available to move immediately (I would never consider accepting any applicant available immediately), inspect their present housing, see if they are concealing pets, are they considering buying a home in the near future, are they married or just living together. find out where the lies are in their applications....every applicant lies.Consider length of employment, double or single income, likely hood of upcoming family situation changes, exact credit scores, interrogate their previous landlords and talk to their present landlord to confirm they have given proper notice.

We don't mind pets and think a person with a dog may stay longer.

Fireplace, some additional granite in laundry room, pet door etc.

Something that tells them the requirements needed to be able to rent the property, like monthly income requirements, no pets, security deposit, etc... so people don't waste their time paying the application fee?

I allowed her to have a pet, as it was a tiny chihuahua.

Don't fight it, figure out how to deal with your biggest pet peeves (indoor furniture outdoors, for me) and let the rest slide.  

-property abandonment clause-if allowing pets, "normal" pest control is tenant responsibility-define what constitutes a guest and an occupant-right to enter quarterly for pest spray and/or filter change-emergency provision to enter with zero notice in certain situations-only cars registered and functional can park in driveway, and no working on cars such as installing a new engine.

It can just say something like: 3 bedroom houses for rent; we love pets; call XXX-XXXX.

and then some old cabinets Family room (*could easily be turned to 3rd bedroom in each) Living room Both have porches Droppped ceilings Basement Split utilities Washer and dryer Foundation field stone old but sound Wood "telephone" pole columns Both tenants have pets.