Just so this is understood: Mutts are NOT inherently healthier than purebreds. They are wild cards in the genetic health department.
People usually try to back this assertion up with "Hybrid Vigor" However, Hybrid Vigor refers to cross-species breeding (and only to the ideal results of those breedings). Not CROSS-BREEDING. Dogs of separate breeds are the same species and prone to most of the same hereditary diseases. Some breeds more so than others They do not benefit from the theory of Hybrid Vigor in the event of mixed lineage.
Add to that the fact that most mutts come from poorly bred, untracked lineage... Which increases chances of hereditary disease since no effort is made to prevent affected dogs or dogs likely to produce affected puppies from breeding. Mutt puppies can still inherit hereditary diseases from BOTH parents and ANY lines from ANY breed bred into them in recent generations.
So if you have a Mutt Puppy... They could have 2-6 or more breeds all mixed into them. They can inherit BAD traits and hereditary illnesses from each and every one of those lines/breeds. And if more than on of those lines share a common illness, even more likely.
It is a MYTH that mixes and mutts are healthier in general than purebreds. They are equally as prone to inheriting defects and disease as any purebred dog. The difference is that responsible breeders today, carefully track their bloodlines and any illnesses that pop up in their lines and try to remove those hereditary diseases from their lines. Something haphazard or irresponsible breeding can not achieve.
That being said, It is a FANTASTIC idea to adopt. Mutts and mixes can be just as amazing family dogs. So can the purebreds you find in the shelter. But it is not true that Mutts/Mixes are healthier in general and a potential adopter needs to consider potential health issues and plan/save for them just in case. (something you should do even if purchasing a purebred from a reputable breeder.)
ETA: Even in the case of Hybrid Vigor... There can be Outcrossing/outbreeding depression. Especially in a breeding that produces multiple offspring... Some of the pups may get the best of the breeding, some the worst and some average. Such breedings for improvements will not likely produce all offspring superior to their parents. It could potentially produce all offspring inferior to one or both parents.
ETAagain: Mixed breeds from intentional and carefully selected breedings, however, can potentially benefit greatly from the cross. One very serious issue in many pure breeds is the severely limited breeding pool. Introduction of new stock can greatly benefit a line or breed if done carefully. It can also have severe damages as well.. (big example: The mixed offspring produced by BYBs creating misshapen mixes and marketing them as "pit bulls". They introduced many negative traits and created dogs with skin problems, an increased risk of mange, deformed skeletal structure with an over-sized frame, deformed heads, ect. The resulting dogs suffer for the cross-breeding done to their lineage.) A good example resulting from cross-breeding: The Doberman Pinscher. Very carefully produced for specific working goals and purpose. Though it now suffers from poor past breedings and a limited breeding pool.)
