Mondor's Cord is inflammation of a blood vessel. It isn't considered a "risk", per se. It heals on it's own, and causes no permanent damage.
The small vein that's visible is called Mondor's Cord. Mondor's Cord is not a complication. It resolves on it's own. Ibuprofen and warm compresses may be used for discomfort, which is usually fairly minor. One or more "cords" may be present, and is may also be seen in the arm (extending from the armpit to the elbow).
If you get Mondor's Cord, you should consult with your surgeon before taking Ibuprofen, which thins the blood. Some surgeons don't want their patients taking anything that thins the blood for a few weeks after surgery, while other surgeons are more lenient.