"Don't take no chances, two shots in the head a piece!"
When Al Neri takes out Barzini, he shoots the two guys up close (one guy gets two bullets the other just one). Then he shoots Barzini twice in the back from long range.
Now consider this: Vito was shot five times in the back from close range and lived. What if Barzini had made it through alive?
Surely Clemenza would have given Neri the same advice? Also, what would have happened among the five families had Barzini lived?
Well Neri had to shoot Barzini from far-range, which surprises me that the pistol he was using was accurate from that distance. Obviously, it would be too risky to climb those stairs and finish Barzini off.
I always wondered why Neri started opening fire when he did instead of letting Barzini get closer. I think this could be chalked up to another "artistic license" where FFC wanted Barzini's death to be dramatic.
As for not shooting the other two properly (bodyguard, chauffer), he had to shoot Barzini too who was running and I don't know why he didn't finish 'em off after before running into the car though.
