Reply #14: As JCMACH1 noted, it is a problem when certain genetic diseases are present.

[Gormy Cuss]

Marrying your cousin is not much of a risk if there are no nasty little recessive disorders coded into your genes, but if there are it can be a different story. There's evidence that close consanguinity in the polygamist Mormon groups has lead to an unusually high rate of fumarase deficiency, for instance.

We're fairly well protected in our mobile society because we tend not to intermarry among close cousins. We'd need to pick a mate by chance who had the same recessive gene, and that happens.