A dog's mouth is no cleaner than a human's, they just have different dental microbes, according to LiveScience. The mouths of both species are teeming with bacteria that cause similar dental illnesses.
Both dogs and humans are affected by periodontal disease, but the species of bacteria that cause it are slightly different, explains LiveScience. However, dental cavities are much more rare in dogs because their diets are usually low in sugar, making a dog's mouth a more inhospitable environment for the S. mutans bacteria that thrive off of sucrose. People are unlikely to become infected by a dog's germs, but some bacteria can be exchanged between the species, notes Mental Floss.