Bobby Fleet refers to Andy as "Hyrum." This was '50s slang for a sweet, funny and often naive boy of strict religious upbringing, typically Mormon.
The little boy with the dog pictured on the jail cell calendar is Ron Howard's real-life younger brother, Clint Howard.
Bobby Fleet's vehicle is an extended 1947 Cadillac.
Bobby Fleet would appear on the series three times. In this episode, Bobby Fleet was played by Henry Slate. In Season 1, episode 31 "The Guitar Player Returns," Bobby Fleet was played by Herbert Ellis. In season 3, episode 8 "The Mayberry Band," Freddy Fleet (not Bobby Fleet) was played by Joseph Sirola.
The guitar Jim is playing is a Harmony Archtone, a common student instrument from the 1950s and 1960s.