Can an STD cause serious harm to an unborn fetus?

Yes. In particular, syphilis, hepatitis b, hiv, herpes, gonorrhea, and chlamydia can either cause harm to the developing fetus or be transmitted to the fetus while it is developing. Most of these stds are screened for at the first prenatal visit, and many can be treated to avoid harm to the baby. If you are concerned about your exposure to stds in pregnancy, see your healthcare provider!
Absolutely. Many stds can cause harmful or life threatening injury to a newborn. For example, chlamydia is the most common cause of blindness in the "third" world. Herpes can be fatal to a newborn, and syphilis can cause a range of problems including death. If std is suspected in pregnancy it is of utmost importance to get evaluated and treated if present.