The 'inbreeding' argument doesn't, and has never, held water. Not that I'm about to jump my sister; but as a point of science its not terribly significant. Cousins can actually have closer DNA than siblings; cousins are often allowed to marry (varies state by state). The idea that only horrible monsters will result is silly; its how all purebred farm animals are created.
The main argument against incest that I know of pertains to recessive genetic diseases. Suppose one parent has a recessive disease, and the other does not (P generation). Then F1 generation may have carriers, but will not display the disease. If F1 mate together, however, then the F2 generation may contain individuals who are homozygous for the recessive allele, so they will display the disease.
There was a case in which this happened, the "Blue Fugates" [0], who had a particular recessive disease[1].
This argument made sense before genetic screening was available, but falls apart with genetic screening, since you could screen the siblings to see if they are both carriers.
