At the beginning, when Kent walks along the balcony, he throws an apple core from a fair distance that hits the back of the barman's head with great precision. However, before the cutaway shot that shows the apple core's final impact, it can be seen that it was, in fact, veering to the left of the barman's head and would have missed him entirely.
Tom Destry (James Stewart) makes the typical movie actor mistake of shooting his pistol at something by jerking the pistol and firing the gun at the target at the same time. In reality, if a shooter did that he would be moving the pistol off line and would miss every time, because the motion of the hand would impart a vector onto the bullet that would make it miss. Also, shooting that way is incredibly inaccurate. A real shooter would level the pistol at the target and then pull the trigger. Audie Murphy, a trained marksman, shot his pistols correctly in the remake Le nettoyeur (1954).
When Destry first demonstrates his ability with a firearm by shooting at the knobs on the sign, he shoots a total of seven times. Although he is holding two Colt "Six-shooters", one in each hand, he fires only the pistol he holds in his right hand. Thus, he fired at least one more round more than the pistol could fire.
Destry is shooting the knobs off of a sign to show his expert marksmanship and his knowledge of how to handle pistols. Before he shoots the last knob off the sign, the Colt pistol he is using goes off prematurely and shoots into the air. Therefore, he could not have shot the last knob off the sign.