My first checks I do on serious applicants are to my free on-line sites -- my state's court data base for criminal and Facebook to see if they have posted photos of undisclosed pets.  

This lady discriminates against non-pet owners.

It can withstand a lot of abuse, especially pet stains.

Like allowing pets or really updating everything.

Both women are on the lease), and the tenant on the second floor a young man in his 20s (whose mother is a co-signer on the lease).Tenant of the second floor unit, has a Pitt bull on premises (not on the lease and it says no pets unless there is written addendum added to the lease). 

We would of course charge a pet fee, background check/screen the individual and the rest of due diligence if we decided that, but what is your opinion? 

Thoughts on how to approach this situation....I am screening a potential tenant...good credit, clean background, verifiable gross income 3+ times rent, no pets, and seems like a neat & orderly kind of person. 

That's one of the reasons I don't allow any pets in my houses. 

I manage an HOA that does not allow pets, to include indoor pets like cats. 

Your roommate's pets trashed the place and that probably was paid for by your parents.