My doctor told me that my baby shows evidence of Rh disease or incompatibility. How serious is this?
First off, the basics of blood typing: Red blood cells have proteins (antigens) on their surfaces that can be recognized by the body's immune system. A, B, and Rh are the blood group antigens, and each person's blood type is a reflection of the antigens on her cells. Your blood type is defined by the A and B antigens (absence of both is called O) and by whether the Rh factor is present (referred to as positive or negative). From what you say, it sounds like you are Rh negative.
Each person recognizes her own blood cells as "self" and doesn't react to them, but is capable of making antibodies to fight off antigens that are viewed by her body as foreign. Most of the time, even in pregnancy this doesn't cause a problem, because fetal and maternal blood doesn't mix together. The placenta keeps the two bloodstreams separate as it allows nutrients and oxygen to be shared. But if some Rh positive fetal blood cells do get into the mom's circulation (and the mom is Rh negative) and she doesn't receive the proper prevention, she may make antibodies against the fetal cells. These antibodies can then cross the placenta into the baby and fight the baby's red cells, leading to fetal anemia (low blood count). Usually the mom's response is weak at first and doesn't cause severe anemia in the first baby, but Rh sensitization can become a serious problem in subsequent pregnancies.
Luckily, preventive measures are usually effective. All Rh negative moms are treated with Rh immunoglobulin (Rhogam) to prevent Rh sensitization. Rhogam rounds up any stray fetal blood cells in the mother's circulation and removes them before she can start to react to them. In this way, she never "sees" the Rh factor, and her immune system doesn't learn to react to it. Rhogam is given in the third trimester and after delivery, after any significant vaginal bleeding in pregnancy, after miscarriage and abortion, and any time there is a risk that fetal cells entered the mom's circulation, like after a car accident.
If a mom does become exposed to Rh positive fetal cells and develops an immune response, Rhogam is no longer effective, and more complex measures must be taken to protect the baby.
If you are truly sensitized, the baby will need to be watched closely for signs of anemia, so that treatment can be offered before serious consequences develop. Usually ultrasounds every few weeks, with special readings called Doppler flow, are used to assess for fetal anemia. Sometimes actually drawing blood from the baby (cordocentesis) and/or transfusing the baby (through the mom's abdomen) is required. Rhogam has been so effective that most obstetricians don't see Rh sensitization any more. Maternal-fetal medicine specialists are the experts at caring for Rh sensitized moms.