Also, this used to cause trouble with phone operators connecting phone calls between USA and England: "are you through?" could mean either "are you connected?" or "are you done with the conversation?"

Punt is an interesting one. I think the original meaning was "offer". I've seen it used this way in the British press: The company is punting a new product. This could have been the original meaning in American football: to punt the ball is to offer it to the opponents. But since a team punts when they have given up on making a first down, the meaning of punt shifted to "give up".