I have a 6 week old male kitten; his mother had a litter before his, and the person who owns her kept one of them, so the son and mother bred. She only had three kittens. One passed unfortunately but the other two seem okayish. My male kitten has kind of a smushed face and his little legs seem to stop him from doing a lot. I am very worried that he has more problems than I know of. Can anyone help me and tell me what all problems he can have knowing the mother and son bred?
Take the kitten to the vet. As soon as you acquire any new pet, you should take it for a vet visit as soon as you can, so you can make sure it's properly vaccinated and so forth.
As for your concerns that the cat is inbred, it is true the cat is at higher risk of bad genetics due to its mother and father being so closely related. If, for example, the mother has a undesirable recessive gene, the son had a 50 percent chance of inheriting it from mom. The odds then of the kitten of the mother and the son inheriting two sets of the bad recessive gene would be 12.5 percent, and the kitten would actually be affected by the bad gene, as opposed to a potentially minute chance if she had bred to an unrelated cat, depending on how rare the gene is in the population. The chances of the kitten inheriting no bad genes is only 37.5 percent, as opposed to if the mom were bred to an unrelated male, in which case the chances could be near 50 precent, depending on how rare the gene is in the population.
What exactly you might expect if the kitten did get a poor genetic hand is impossible to say, as we're talking about an increased chance of practically all genetic illnesses, since we do not know the mother's genes.
But, as you can see, the odds are still in the cat's favor of not inheriting an illness due to recessive genes, and furthermore these odds are calculated assuming the mother has some undesirable gene that works as a simple mendelian dominant / recessive gene. The mother could have no such genes, and therefore the odds of inheriting some undesirable trait are possibly even lower than what I have calculated. However, I should also note that odds may also be worse if mom and son are purebred cats or crosses of purebred cats, since purebred cats tend to have higher rates of genetic illness.
Even still, in conclusion, despite all the warnings people give about the dangers of inbreeding, it's by no means a guarantee that something will be wrong with the resulting offspring especially in just one generation of inbreeding. The real risk comes in when people start inbreeding across multiple generations. The reason people emphasize the danger is because irresponsible breeders will do this on purpose in order to make shortcuts with selective breeding, and so the chances of animals becoming inbred are pretty high due to human ignorance.
However, that being said, it sounds like the kitten could possibly have brachycephaly, which basically means the short nose seen in certain cat breeds like the Persian. If the mother and father don't naturally have brachycephaly, it could be a sign of a developmental problem in the kitten, which may or may not be due to a genetic illness. Again, the kitten should be assessed by a vet as soon as possible to determine if this is the case, on top of the normal need to take all new pets to the vet.