In general the folds are healthy cats if breeded responsibly. As mentioned here before, the breed was forbidden in 1973 due to deafness and ear mites. Both reasons are not reproducible. Deafness was a problem, but only because of the white coat of the early folds. White cats are often deaf because of another gene that is inherited together with the whit color. Ear mites are a general health care problem and don't have anything to do with the folded shape.
More critical are the problems with bones a breeder found in some animals. Tails and large bones were shortened and thickened, claws grew abnormal. The geneticist Oliphant Jackson took one of the animals and used it for test breedings. The results were scientifically not really worthful due to incest breedings and a low amount of litter/offspring he examined. At least he found that the gene for the folded ears was inherited in a dominant way, so only one parent has to have the folded ears. The symbol Fd is now used for cats with the folded ear gene whereas fd is used for straight ear cats. Most of your Scottish Fold cats will have the genetic pair Fd/fd (one from mother, one from father) which means the dominant Fd gene will lead to a folded ear phenotype. A normal cat always has fd/fd genes. If you breed two folds with each other kitten could get osteochondrodysplasia (OCD) a severe bone affecting disease. Therefore responsible breeders only use one Scottish Fold and another breed (like British Shorthair or American SH or domestic cats). So that only one parent can give the Fd gene to the offspring. Some scientist say that all Folds will suffer more or less from bone problems. However this is speculation and scientifically not proven.
Treatment: Cats with OCD profit from x-raying of the affected bones (see Hubler et al.). Animals with less severe symptoms can be treated with medication like glucosaminoglycane and pentosane. With meloxicam the pain can be reduced. Sometimes surgery (osteotomy, arthrodesis) can be useful, too. Cats with OCD should not be physically stressed, so big steps and jumps should be avoided.