This is the second appearance in the series of Eddie's father George, played by Karl Swenson. The first appearance occurs in Voodoo Magic (1958), also played by Karl Swenson. George would later be portrayed by George Petrie in season six: The Credit Card (1963) and Summer in Alaska (1963).
This is the second time Madge Kennedy appears as Aunt Martha. She appears in this role throughout the series for a total of five times.
The actor playing the conductor, Joseph Crehan, is wearing a Conductors hat with "C. P. & St. L" lettering. Which stands for Chicago, Peoria, & St. Louis Railroad, which was a railroad in Illinois that operated between Pekin (near Peoria) , and Madison (near St. Louis). It's property was sold at foreclosure to several new companies in 1920, so it wasn't in operation under that name at the time the boys were riding the train when this aired in 1958. The northern portion of the line became part of the Illinois and Midland Railroad and a small portion of the line near St. Louis is owned by Norfolk Southern Railway. The rest of the line was abandoned. This points to Mayfield being in the Midwest.
During their visit with Aunt Martha, the boys went to the beach and found a starfish, a hint that Mayfield isn't far from an ocean.