Half dollar with Kennedy on one side and Franklin on the other Was this a mistake at the mint?

It's a magician's coin made by cutting apart 2 genuine half dollars and joining the heads sides. Coin dies are "keyed" so that 2 heads or 2 tails sides can't be inserted into a press at the same time.

Double-sided coins sell for a couple of bucks at novelty shops. Coin collectors aren't interested in them, but the original coins' silver content may make your piece worth at least a few dollars for its metal.