According to director Howard Hawks, all the animal captures in the picture were performed by the actual actors; no stuntmen or animal handlers were substituted onscreen. The rhino really did escape, and the actors really did have to recapture it - and Hawks included the sequence for its realism.
Composer Henry Mancini wrote a brief piece of incidental music to go with a scene where a baby elephant is taken for a walk. The simple little song became an international hit as "Baby Elephant Walk", and has been recorded by a large number of artists and in many different styles.
Much of the action sequence audio had to be re-dubbed due to John Wayne's cursing while wrestling with the animals.
One evening, Red Buttons and John Wayne were playing cards outside and a leopard came out of the bush towards them. When Buttons mentioned the approaching leopard, Wayne said, "See what he wants."
Many critics carped that the film seemed like a lazy vacation for Howard Hawks. They were partly right - there was no finished script and Hawks relished the chance of filming what he wanted on location in Tanganyika--now Tanzania--far away from the watchful eye of the studio, happily burning through their six million dollar budget.
Howard Hawks: He appears in at least two scenes in the movie: The first appearance is in the back of the truck when they are chasing the Rhino toward the end of the movie. He is standing on the right wearing a hat and mostly looking down/back. The second appearance is when they are standing listening to Pockets read the letter from Dallas. He walks through the hall behind the scene.