When a baby is Rh positive, but the mother is Rh negative, there is a risk of developing hemolytic disease of the newborn. This condition occurs when the mother's antibodies attack the baby's red blood cells in subsequent pregnancies, which can lead to serious health issues like anemia or jaundice in the baby. It is crucial for Rh-negative mothers carrying Rh-positive babies to receive appropriate medical care to prevent or manage these complications.