During the "Why a duck?" sequence, it seems that Groucho Marx almost calls Chico Marx "Ravelli", which is Chico's character in Animal Crackers. Since they were shooting The Cocoanuts in the morning and acting in Animal Crackers at night, this mix up is understandable.
Filmed at Paramount's Long Island Studios in Astoria, Queens Borough, New York City. Sound films were still so new that soundproofing was not installed, so the film had to be shot in the early hours of the morning to reduce outside traffic noise.
All paper used as props is soaking wet. This was done to prevent overloading the early sound equipment with paper-crinkling noise.
The sight gags in which Harpo eats the lobby's telephone and drinks from the inkwell were not in the original play. Robert Florey improvised the gags to give Harpo Marx bits of silent business to do. (The telephone was made of chocolate, and the inkwell was filled with Coca-Cola.)
The first use of the overhead camera shot (from the roof of the sound stage looking down at the dancers forming kaleidoscopic patterns) is usually credited to Busby Berkeley, the Broadway dance director whom Samuel Goldwyn brought to Hollywood to stage numbers for Eddie Cantor comedies. But a year before Busby's appearance on the scene in Whoopee! (1930), the overhead shot is used for the first time in an American sound film in The Cocoanuts.