Dog's mouths are cleaner than a humans, on there are only 5000 bacteria in a dogs mouth on average, while in a human mouth it is far more variable (and usually higher and requires cleaning).
Of course, if a dog has just taken a dead something in it's mouth, already decaying for some time, then yes, a dogs mouth is dirtier.
But this is managed by special enzymes, so it stays at a near constant of 5000.