Can acetamidophen or tylenol, cause bruising?

No bruising is not one of the common side effects.

But if you take it over a long period of time, it can cause liver damage and that would cause bruising.

No, Acetaminophen/Tylenol do not cause bruising unless there is damage to the liver like Kaismama said. But just a note, Acetaminophen and Tylenol are the SAME THING so you don't have to worry about one being worse than the other as they are the same medication.

Yes!! For years I have had to avoid Aceetamindophen, Tylenol and mostly all pain killers like Aspirin. I will get huge bruises, usually on my extremities. They don't hurt and my doctor doesn't seem concerned. For me it's just ugly to have them. I would mention it to your doctor though.