Birth defects, whether physical, mental, or a combo of both, as a result of incest, is quite rare. It's not like the horror stories make them out to be.
We all have bad recessive genes that for whatever reason, doesn't surface. When we marry out of our bloodline, that recessive gene stays recessive...or at least you hope your spouse's bloodline also doesn't have that recessive gene. However, marrying within the blood allows that recessive gene to more likely surface. So let's say, maybe in the past 3-4 generations, a family had only 1 person that had asthma. But then down the line, two cousins have an incestuous relationship, and then most of their children have asthma.
It works like that. It's not like an incest is going to produce swamp thing. Most incestuous couples may have a lifetime of normal children just like other non-consanguine couples. Because the DNA is simply being recycled from the same source or whatnot, between two related male and female, the chances of the recessive genes (that were already existing) just simply has more chances to come out.
It's like grabbing balls out of a jar; there's 98 blue balls and there are only 2 red balls. An incest creates a brand new jar (a baby) with 100 balls again, but this time there are 4 red balls.