The roles of "The Redcoats" (Ernie and Freddie) are played, respectively by Chad Stuart and Jeremy Clyde who are also known as the folk rock duo, Chad & Jeremy.
Chad & Jeremy, who play The Redcoats in this episode, were an actual singing duo who arrived in the US during the British Invasion, riding the coattails of Beatlemania, with similar long haircuts and British accents. They had several hit records, such as "A Summer Song" and "Willow Weep for Me" in 1964, the year before this episode was filmed. The duo played a similar role in an episode of "The Patty Duke Show" ("Patty Pits Wits, Two Brits Hits") in the same year of 1965. (The duo of Chad & Jeremy was sometimes confused with the singing duo of Peter & Gordon, because they were both composed of two young British men with long hair, one member with glasses, one without, who were hitting the charts at roughly the same time, during the British Invasion. But Peter & Gordon had the advantage that Paul McCartney, of the Beatles, occasionally gave hit songs to Peter, because he was dating Peter's sister. Those McCartney hits included "Woman" and "A World Without Love". )
Trudi Ames, who appears briefly as a crazed fan of The Redcoats, played the nearly identical but much significant role of Ursula, the Birdie-crazed teenage president of his fan club in the musical "Bye, Bye Birdie." That film also starred Dick Van Dyke.
Ernie and Freddie dedicate a song they are about to sing on The Alan Brady Show to Rob and Laura to thank them for their hospitality. The duo says that the song they're going to sing comes from their friends Chad and a Jeremy back in England leading to a hysterical laugh from the studio audience. This of course is an obvious reference to the duos real names Chad and Jeremy.
Many of the tactics used to hide the Red Coats, such as sending decoy limousines and hiding the band members in laundry trucks, were actual tactics used to transport The Beatles during the height of Beatlemania.