The title of this episode is a pun on one of Bud Abbott & Lou Costello's final movies, Dance with Me, Henry (1956).
After falling while learning to dance, Herman gets a new respect for Lawrence Welk. On The Lawrence Welk Show (1955), whenever the orchestra played a polka or waltz, Welk himself would dance with the band's female vocalist, the "Champagne Lady".
Herman croons "Singin' in the Rain", a song with lyrics by Arthur Freed and music by Nacio Herb Brown, published in 1929. The song became a hit and was performed for the first time on film by Cliff Edwards and the Brox Sisters in the early MGM musical The Hollywood Revue of 1929 (1929).