Purebred cats that have been inbred will have the very best and very worst genes in that line. However, if the breeders know what they're doing, they will not breed a problem to a problem. They have access to the pedigrees and they know what they're getting in a litter. (Nature can always come up with surprises, but not as likely with a breeder who's knowledgable) The buyer should ask many questions, and insist on a health report. Obviously you would not want to get a Siamese kitten with crossed eyes or a Persian with chronic runny eyes or nose. However, in my opinion, those problems are a result of bad breeding. Know whom you're dealing with, and never buy from a pet store or a kitty or puppy mill!
Find a reputable breeder whose motive to breed is to improve the health and overall good of the breed. (cats or dogs)
With DSH or DLH, you have no idea what the background of the tom and queen is. Littermates will often breed, especially if there's a colony of barn cats. That's not good! I have had moggies with great personalities and health, and I've had moggies with birth defects--internal defects.
Often, people will tell people not to buy a German Shepherd dog, for example, because hip displasia is common to the breed. That's not entirely true. All large dogs are more likely to have that problem than a lap dog. It depends on where you're getting the information, whether it's a cat or dog. Read what you can, and know the disposition and common health problems of the cat or dog.
Buy sensibly and buy the one you love, who seems to love you!