Andy and Barney were related – for three episodes.
When the show first launched the writers had Sheriff Taylor and Deputy Fife acting as cousins. They gave up on this concept after three episodes and just hoped nobody would notice. We did, however, because we have enough trivia to develop one of them sustainable cities of pop culture references. You are welcome!
The introduction was a love letter to Andy’s own father.
In the introduction of the show you can see Opie throw a rock while Andy immediately nods with a small smile. Apparently this was his father’s personal acknowledgement for just about everything: a slow, small head nod.