I must protest MMJ.
I think it just comes down to how responsible the tenants are,regardless of whether they have a dog or not.
It's up to the real estate the landlord is going through to adequately check if the tenant is going to be responsible or not and if they have decent references for themselves and any pets they may have.
If the tenants don't have good references then they will not look after a property and having a dog there with them will obviously only cause more damage, the same as if they had children with them.
I believe if people are responsible and caring tenants, then they will make sure their animals are properly trained and a landlords house is looked after.
Renting to someone who has a dog may be risky to some landlords but so can renting to someone who has children.
If you think dogs can't count, try putting three dog biscuits in your pocket and then giving Fido only two of them. ~Phil Pastoret