Many things could go medically wrong to a developing embryo/fetus when produced by 2 blood related persons. That doesn't mean it will, but it certainly can. The closer the relation the more at risk you are and it has certainly been proven that 1st cousins are considered closely related if by genetic factors alone, despite the moral and legal aspects of inbreeding. Inbreeding meaning; To produce by closely related individuals.
There is a long-held view among geneticists that inbreeding tends to concentrate undesirable or even lethal recessive genes, which might otherwise not be expressed. Mental retardation may sometimes be the outcome of such matings. According to many scientist's in Genetics programs at different universities, the genetic risks may actually be quite high. One article revealed a higher than expected incidence of abnormal neuropsychiatric findings among patients who were the child or younger member of a blood relative relationship; e.g., a higher incidence of seizures and lower IQ.
For more detailed genetic information relating to inbreeding or incest, I suggest you contact a Department of Medical Genetics. Or call the American Association on Mental Retardation (202-387-1968).
TO SPECIFY FIRST COUSIN REPRODUCTION:
Children of first cousins have F = 0.25, and so are identical by descent at 1/4 of their loci. If any of these loci affect peri-natal health, mortality rates of inbred children will on average be higher. Several studies comparing mortality rates among children of first-cousin marriages versus children of non-relatives have been made, based on extensive parish records of marriages [which indicate consanguinity], births, & deaths. In each case, the early mortality of the children born to related parents is higher. The reduced health of inbred individuals is called inbreeding depression.
Hope this helps!!