Blood clot. Any birth control method that has estrogen in it has rare, but serious, side effects like blood clot, stroke and heart attack. Keep in mind however that getting pregnant has a risk of blood clot that is 6 to 10 times greater than birth control. Also to keep things in prespective...Driving your car is probably the riskiest thing you do on a daily basis.
Compliance. The most concerning down side is a slightly higher risk of a dvt. There are advantages, the primary advantage of the patch for birth control is the avoidance of needing to remember to take the pill every day.