As more and more adopted dogs are pit mixes, this clause was included in my most recent lease and is very landlord-friendly for mix-breed dogs:
Owner Shall Determine Breed: Regardless of resident’s
representation as to the breed or classification of any animal,
resident agrees that owner shall make the final determination as
to the breed or classification of resident’s pet or animal in
owner’s sole and absolute discretion. Restricted Breeds shall
have the broadest possible meaning, and includes, but is not
limited to, any animal displaying physical traits or characteristics
of any restricted breed animal, whether by observation or by
standards established by the American Kennel Club, or other
applicable association, or defined by any law, statute, or
ordinance.
Furthermore, at every rental I have ever lived in with my dog I have been asked for a pet deposit, proof of vaccination and a picture of the pet. These are very common things that you can easily ask your tenant for. The proof of vaccination sheet is typically from a vet and includes the pet's breed, age and weight.