ABO incompatibity. This is rarely a problem since all obstetricians test for it and treat the baby as well. Your doctor can explain it. Look up neonatal jaundice if you wish to read about it.
Rhesus Factors. If the mother has negative rhesus factor (such as o-, a- or b-) and her previous child was positive (o+, a+ or b+) then there is a possibility that the blood got mixed at birth. This would enable the mother to make antibodies against the rhesus factor of the infant. If the next child (rh +) comes along the mother will be able to mount an immune response against it.