Generally speaking the Mini engine is a strong unit, having said that you should listen very carefully for any unusual noises when starting and also when the engine has reached working temperature. Should a Cooper or a Cooper S have any slight rattle in the top end of the engine, its either the hydraulic tappets (that operate the inlet / exhaust valves) are worn or the timing chain is stretched and isn`t being tensioned correctly, or the tensioner itself is faulty. If you slowly rev the engine up and listen for any bottom end knocking or rattle. If you do it’s very likely the engine has been run short of oil at some time. Also look for any signs of leaks from the engine especially the oil filter housing and / or the sump area that could confirm this. But, with such a vast choice of Minis that are available, you need to walk away from the sale if there are engine sounds that you`re not happy with.