Poor Bert. He has quite a conundrum at the end of this sketch. On the one hand, he can't sleep with Ernie snoring, but on the other hand if he wakes Ernie up, Ernie will start talking again. And probably say something to the effect of, "What did you wake me up for, Bert? That was really inconsiderate!" It really isn't fair, is it?
Nevertheless, things would possibly be a lot easier if Bert would just say exactly what he wants, i.e. "Would you please go and turn off the faucet?" instead of vaguely asking Ernie to "do something" about the water dripping.