Mayor Stoner's house is the same structure that was used for Aunt Pitty Pat's house in Gone with the Wind (1939).
The plot of this episode revolves around Aunt Bee's (Frances Bavier) birthday. Frances Bavier was sixty-years-old (born December 14, 1902) when this episode aired.
The name of the beauty shop that Clara and Bee come out of is "Wakefield." Along with the Carters, they were one of the two feuding families in the county. Throughout the series many of the same family names were sprinkled into the scripts, giving a sense of community to the series story arc. Among them are: Beasely, Gilley, Pyle, Walker, Crowley, Mendelbright and more.
Oddly, Aunt Bee doesn't notice that the box she's opening is *huge* for a bed jacket. It actually contains 24 Mason jars, making it tall and heavy, yet she thinks it contains a bed jacket weighing a few ounces.