Irene Tedrow plays the role of a You Bet Your Life game show contestant named Dr. Jeanette Eyeman. This is a reference to Jack's secretary Jeanette Eymann.
Jack Benny liked and admired Groucho, but was very unhappy when Groucho criticized Benny's writers.
The answer to the question the first couple got incorrect is "Peter Minuit." Two years after this aired, Groucho Marx played Peter Minuit in The Story of Mankind (1957).
Jack Benny makes a comment that Groucho is older than he is, or that at least one of the Marx brothers is older than he is. Jack was born in 1894, Groucho in 1890, Chico in 1887, Harpo in 1888, Gummo in 1892, and Zeppo in 1901, making ALL of the Marx brothers except Zeppo older than him.