Several. Aspirin offers benefits and dangerous side effects. For a thorough discussion of the topic see http://mdprevent.Blogspot.Com/2013/02/dr-oz-and-asprin-is-he-being.Html. Aspirin isn't for everyone and high cholesterol alone may not be an indication to take it. Other factors such as family history of heart attacks and strokes, high blood pressure, obesity, etc. Must weigh in so speak with your doctor.
Bleeding/ulcers. Aspirin can erode the protective lining of the stomach and this effect is mostly independent of whether you take enteric coated Aspirin or regular aspirin, it is the effect of the drug on the protective chemicals in the stomach (prostaglandins), this would then lead to ulcers and bleeding. It can also increase skin bruises. However, the benefit most often outweighs the risk.