What birth defects can an inbred baby be born with?

Any number of issues: babies born from cosanguinity ( meaning from "blood relation" -- being from the same kinship as another person) are at risk for issues that can affect any organ system. Babies should be followed in-utero by a perinatologist and geneticist as well as genetics consult after birth depending on birth issues or issues during pregnancy. Talk with your OB & pediatrician for more info.

Too many to list: If you mean what could be wrong, the list is endless. We are each thought to carry recessive genes for up to 4 metabolic mistakes, stuff that may only show up in 1/50,000 births. If we have kids with a close relative, it is more likely one of those defects will show up. There are in excess of 250 metabolic problems (like PKU) known.