I get that it is expensive and often I am asking them to have almost 5k set aside for the first month, deposit, and possibly 600 pet deposit but I'm looking for tenants who have the ability and financial responsibility to have an emergency savings. 

Think of all the things that could go wrong and see if the lease addresses them: unauthorized pets or tenants, early termination, security deposit, lease violations, late rent, eviction, lawn maintenance, parking, etc.5.

As long as the pet isn't a service or comfort pet - and none of the criteria are Fair Housing issues, you're good to move on...Hope this helps.

#2 No pets?

The next unit was 1 year into a two year lease at $900 per month but allowed to have pets, and turned out to have three rabbits, one dog, and three cats, all in 1000 square feet.

This applies to pets as well.

She also said that it will seal in any pet odors we aren't able to remove from washing.However, others have said it's not worth the expense, and if tenants decide to paint the wall (without permission), we will have to incur the cost to re-paint with the same expensive oil-based paint. 

I allow dogs and like them due to the additional deposit of 600 plus 35/month/pet. 

If they can't answer it easily,  move on.How often they inspect and what action they take if they discover an illegal pet, unauthorized occupant, or housekeeping issues. 

I have discovered that they just got a new puppy and the language in my lease states that no pets are allowed.