Anyone who survives long enough with this weapon to reach a settlement would be best trading in for a real weapon, even a pointy stick would be an improvement.
Training with the BasicsEdit
The BB Gun should never be considered a stand alone weapon. It is in no way a gun meant to be used in combat. In fact, the only serious use of the BB Gun would be for training, trading, or using the base parts for some means of construction.
The problem is, the BB Gun was never meant to be fatal. In the Pre-War days of the past, children would use this to shoot at one another, and obviously they weren't trying to kill each other, they were merely attempting to hit the opposing team or member and thus win the game. Some sources claim that this was a form of early combat training, but do not be fooled by these pseudo-intellectuals. The BB Gun was nothing more than a basic form of entertainment, and thus should be considered as this.
The only way this weapon should be used is for extremely weak enemies. No, not Raiders, because this gun even has trouble taking them out. What you should be using this weapon on is molerats, radroaches, or wild dogs. Even using it to detonate mines is a good idea, and would be better than spending pricier ammunition on it, or endangering yourself by attempting to disarm it.
However, due to its rarity, the BB Gun is be a good collector's item and thus a good item to use during trade. There are reports of some giving these guns to their children as training. It was also used to train rookie guards and soldiers in lieu of live ammunition.
But as was said, one can get a good price for this rare find, a good exercise, or a good means of repairing a lamp or gun or pipes, whatever can find use for the contraption. Just please, please, don't try to kill anyone or anything with it. You will surely fail.