Forbes has a good article on the ten most common complications of cosmetic surgery.

They say the risk of numbness after breast surgery is the most common. Loss of sensation in the nipple occurs anywhere from 10% to 70% of the time.

Seroma is a collection of watery body fluids that occurs most often in tummy tucks. And necrosis is tissue death.

See their informative article outlining the real and common risks of cosmetic surgical procedures.