Blood Clots: A blood clot is a common risk of many procedures, not just cosmetic surgeries. The most common type is a deep vein thrombosis (DVT), a clot that develops in the leg. Most DVTs require medical attention, but are not life-threatening unless the clot begins to move through the veins toward the heart and lungs. A clot that moves to the lungs is a medical emergency and must be treated immediately.