2001 BMW 740iL is sputtering when I accelarate and shaky when idl

A tune-up and throttle body clean-up is a good idea, but mind you on those cars, the valve covers usually leak into the spark plugs and coils, causing the car to misfire. If you are replacing the plugs and find them soaked in oil; replace your valve cover gaskets or you will be back to the same problem soon after the oil soaks the new plugs back up again.

You probably need to change the spark plugs give it a good tune up. The throttle body might also need cleaning. I've had the same problem with my 93 and it was just plugs and throttle body cleaning that was needed.