Can you tell me about the most uncommon type of disease caused by smoking?

Not sure but: In my experience, a severe form of artery spasm induced by smoking, called buerger's disease (or thromboangiitis obliterans), results in complete obstruction of blood flow from the extremities in particular, resulting in gangrene of fingers and toes, and sometimes the entire extremity, often requiring amputation. It can also cause heart attack and stroke.