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.
Bobby Fleet's vehicle is an extended 1947 Cadillac.
The little boy with the dog pictured on the jail cell calendar is Ron Howard's real-life younger brother, Clint Howard.
The guitar Jim is playing is a Harmony Archtone, a common student instrument from the 1950s and 1960s.
Andy mentions "that fella we see on television every now and then," referring to Elvis Presley. In fact, Jim Lindsey is a spoof of that rock star. Elvis Presley was a singer, not a guitar player, whereas Jim Lindsey is a guitar player and never sings in any episode.