The episode "A Black Day for Mayberry" (episode 4.7) featured performances by three members of the Howard family: Ron Howard in his regular role as Opie, Clint Howard in his recurring role as Leon and their dad Rance Howard as a government agent.
In the opening scene, the two Treasury Agents are indifferent to Barney and are waiting in the courthouse for the Sheriff to return. Barney is agitated at being dismissed by them. He picks up the phone book from the Sheriff's desk and begins to nervously flip through it. In several screen shots of Barney holding the phone book, you can plainly read "Mount Airy" on the front cover - Andy Griffith's birthplace and hometown. It has been a long held belief that the fictional town of Mayberry is based on Mount Airy, North Carolina. ***** UPDATE ***** It is a misconception that Mayberry is based on Mount Airy, NC. Andy Griffith explained in an interview that 'Mayberry' is actually based on Pilot Mountain, NC (a much smaller town than Mount Airy) and 'Mount Pilot' is based on Mount Airy (a much larger town that Pilot Mountain).
The first scene in the episode features all three of the Howards in one place. Father Rance plays one of the government men, Ronny comes in to ask Andy for money, and youngest son, Clint, comes along as little Leon.
This is first episode that the third and final location for Wally's Filling Station is used.
This is the only episode of The Andy Griffith Show where all three Howard men appear: Rance, Ron and Clint.