I think I gathered the impression the children of such a marriage would be odd. Reading the information above, I realize it probably is not as dangerous as I thought, but a factor not mentioned is that in certain little sub-cultures or small communities, marriage between cousins of various degrees is not an isolated incident, but a practice that goes on for generations, and that, I think, is not good.
Royalty is an example.
Queen Victoria and her cousin Prince Albert had a LOT of children, who married into royal families all over Europe. The imperial Hapsburgs and the Bourbons of France kept sending their daughters to each other's heirs for generations, thus the children of 1st cousins marrying the children of 1st cousins, and certainly the last Hapsburg Emperor was deformed. Another place consanguinity occurs is in small towns. Your choice of marriage partners is limited, and you may end up choosing someone who is related to you in several ways. I can imagine the gentry of Europe who were limited to their own class for marriage partners, might end up marrying relatives on a fairly frequent basis.