The cleanliness of a dog's mouth is dependent upon the specific dog. Dogs' mouths are filled with bacteria and small particles of anything recently eaten by the animal.
The myth that dogs' mouths are cleaner than those of humans is false. The myth stems from the idea that when a dog licks its own wound or the wound of a human, the wound heals more quickly. Dogs do not have healing properties in their saliva. A dog licks a wound, dead tissue is removed, and healing begins due to the removal of the tissue.
Dogs use their mouths like people use their hands. Dogs explore the world with their tongues and mouths and eat inappropriate things. Many dogs eat feces, dead animals, dirt and other items not fit for consumption. Bacteria from these items is transmitted to dogs' mouths as they are eaten. The amount of bacteria in a dog's mouth varies from animal to animal.
Most bacteria contained in dogs' mouths is not transmissible to humans. Certain intestinal parasites are transmissible. When a dog licks the anus of a dog or cat with parasites like roundworms or tapeworms or eats contaminated feces, the parasites are transferred to the dog's mouth.
Those parasites are then transmitted as the dog licks the human's face or mouth. Owners avoid getting parasites from dogs by not allowing animals to lick their faces, keeping dogs on parasite preventives and keeping yards free of feces.