Purebred dogs have genetic problems because of the way they are bred. If they are purebred then they come from a limited gene pool. When organisms are from a limited gene pool then they tend to not create new genes that can help them fight off problems, their biological systems do not get stronger, they get weaker.
It does seem that purebred dogs have more genetic problems than mutts. Having owned both, I can attest to the fact that the purebred dogs I have owned have had far more problems with vision, bone structure, and health in general than the mutts I have owned. Perhaps the breeding process with purebred dogs keeps the blood lines too close. I'm really not sure what the cause is. Perhaps it's sort of like with children - the more they are exposed to, the more immunity they develop. Mutts are probably not as sheltered as purebred dogs and develop more strength in order to survive.
Those of us who grew up owning dogs have learned that a purebred dog is less vigorous, more prone to rather exotic genetic problems, and all around less sturdy. While "mutts" are not socially acceptable in some circles, and will never be seen at Westminster, they are playful, sturdy, and quicker to learn. Rarely do you see a mutt with genetic problems.
We are getting so sophisticated about our canine friends that we have begun to breed them into such a specialized class that their genetic problems come with them. Flaws in breeding, even in humans, are meant to be minimized as different strains intermingle. Usually this is more healthy than pure breeding which accentuates the flaws over time.
I have had dogs for a little over 30 years of my life. My mother still breeds a few different 'pure breeds.' I have noticed time after time that the mutts that I get from the shelter as rescue dogs live through stuff that I wouldn't believe. I have a mutt now that is some type of collie/german shepard mix that has eaten pills, chocolate, got herself electrocuted by chewing on wires, stuff that leaves me in a state of constant panic. No only does it not kill her it doesn't seem to phase her. The vet didn't even believe she had eaten the bottle of pills until he tested her blood due to the fact she was behaving normally.
I have a mixed dog I got from the streets and he is a tough doggie. I have a certified purebred that I got from my late aunt and let me tell you I regret it. The dog need special care and constant attention. My street dog is so resistant and requires only a pat on his head.
The real point is to quit marrying your cousins and people who are very identical to you. Because you children will pay not you.
I think that purebred dogs would have much less health problems then mutts. Mutts are combining different breeds and you don't know how the cells etc are going to interact with each other. There is a lot of things that could factor when mixing different genetics etc. With the purebred you know completely what is in the Dog.