Sorry to be contrary, but that's entirely untrue. Putting aside the straw man you created, there is no statistically significant evidence presented in any properly conducted studies (key word is properly, the oft-cited one from a few decades ago has been proven to be poorly conducted) to suggest that children of incest have any more genetic mutations than other children.
And I also think you don't understand how genetics works. Nearly every person on the face of the planet has some bit of mutation; it's a natural part of the genetic process, and it's what the theory of evolution is based on. Every new generation has a little more variation because of some differences in the genetic code of the new generation. Sometimes these are harmful, and when this happens those with the harmful defects generally don't live to pass on those genes. It's kind of like trial and error on a planetary scale. However, sometimes such mutations are helpful. The sickle-cell gene became so prevalent because, though it produced other large problems, it provided a resistance to malaria, a highly common disease in the area of Africa it was most common in. Still, the vast majority of genetic mutation doesn't produce any discernible differences. Much of the genetic code is stuff that's never even used, so the mutated genes don't really do much; other times, the change is slight or something that is already common.
On a genetic level, though, there's no reason why incest would produce any different results genetically speaking than any other combination. In fact, incest is quite common in animal populations; if it was something that harmful to the offspring, it would have died off long ago.
Again, though, it's not something I support; merely something I tolerate. I think it's best to try to think about things from an objective standpoint even if I personally find such things absolutely disgusting.
