Dangers of inbred cats?

I've never seen an inbred cat, but I have seen inbred dogs before. I was watching an episode of Animal Planet's "Animal Cops" and this guy had an inbred dog whose eyelashes were inverted (the lashes would scratch his eyes), which really freaked me out. I think that if one is to breed pets and keep them, they should neuter/spay the litter. If the litters are fixed, they should be given away.