In an earlier episode entitled "The Manhunt," Captain Barker promises to send Andy a magnetic map like the State Police use. Barker apparently made good on his promise, since the magnetic map may be seen in the Sheriff's office in "Mayberry on Record."
As Ellie stands at the soda fountain, a poster for Diced Cream can be seen on the wall behind her. Diced Cream was a cubed, single-serving ice cream product that became popular starting in the late 1940s. The company eventually went out of business after being taken to Federal Court on price-fixing charges.
The band 'The Country Boys' appears in this episode. They made an appearance later, in "Quiet Sam." The shorter, dark-haired guitar player is Clarence White, later to join the rock band 'The Byrds' in 1968.
The calendar in the office is consistent with December of 1960.
Inside Walker's Drug Store, the TV Guide with Lucille Ball on the cover (which appears several times in the series) is seen when Opie enters the store. The Andy Griffith Show was filmed at Lucille Ball and Desi Arnez's studio, Desilu.