Look at this again and tell me Sherlock doesn’t know how to use a gun.  (Remember that last one was behind his back!)  Granted this is only from about 20 feet away, but YOU try putting a bullet through the eye dot of a smiley face (twice!) and see how well you come out.

And John (according to ACD) is an even better shot.

AQ’s theory about John not being in the medical corp at all makes more and more sense.  Where the hell does a doctor even find time to get that good?