What are the typical side effects of exercising too soon after giving birth?

Increased bleeding. You may get possibly increased bleeding from the vagina, as the clots in the uterus may be soft and not so strong to control it and increase in motion may help them get dislodged. Also, there may be some more discomfort in the abdomen.
Depends. Generally exercise after giving birth is allowed. However, blood loss during birth may lead to anemia, which is low red blood cell count, therefore causing fatigue and lightheadedness. Also, if there are any wounds that need to heal it is not a good idea to exercise until fully healed, especially if you had a c-section. It is best to get the ok from your physician before exercising.