At the beginning when Gomer visits Bill's Diner, the building used for the exterior shots is Wally's gas station from the The Andy Griffith Show (1960) with new exterior dressing.
The basic theme of this episode was copied from Goodbye, Dolly (1967), which aired almost one year before this episode. Dolly, the horse, appeared to be the same horse in both episodes.
Per the parody in the title, the original Broadway production of "Hello Dolly!" opened at the St. James Theater on January 16, 1964 and ran for 2844 performances, setting a Broadway longevity record. "Hello Dolly!" also won the 1964 Tony Awards for the Best Musical and Best Score. The original Broadway production is the seventeenth longest running show ever.