Bleeding. Although the most worrisome side effect of warfarin is bleeding, you can minimize that risk by making sure that the "thinness" of your blood is tested with an INR regularly. If your INR is always between 2 and 3, your risk of bleeding is substantially reduced.
Blood thinner. Its a blood thinner, which makes you more prone to bleeding. Imagine an injury to a serious organ, and we can't readily stop the bleeding. Having said that, the medicine does have important roles depending on the condition.