If the landlord lives on your property, and it is the landlord's dog, then a large enough amount of dog feces could constitute a warranty of habitability issue - at the very least you may have a claim for the lost rental value from the inability to use the backyard due to the dog feces.

If its another tenant's dog, then the tenant should be picking it up. If the landlord wants to pick it up for the tenant, then they could do so. If it's a third party all together, then landlord isn't responsible for the breach of quiet enjoyment caused by third parties (even after the new landlord-tenant rules go into effect).

Finally, most leases have a clause to allow the landlord to come on the property, so I would review your lease for specific rights.