In supplemental information on the DVD mention is made that Keenan Wynn and James Whitmore neglected to rehearse their "Brush Up Your Shakespeare" number more than once or twice because they thought it was silly. When it came time to shoot it they made numerous fumbles and mistakes which the director thought was on purpose. He later complimented them on making it look like something a couple of thugs would perform. They never told him the truth.
Even though Hermes Pan is the credited choreographer on the film, the steamy duet between Bob Fosse and Carol Haney in "From This Moment On" (which includes Fosse doing a complete back-flip) was choreographed by Fosse himself, and lasts only 66 seconds. But it is the sequence that made critics take notice of the future award-winning choreographer and director.
For the famous spanking scene, Kathryn Grayson and costume designer Helen Rose played a joke on Howard Keel - Rose put a wooden board under Grayson's costume.
Choreographer Hermes Pan makes an appearance as a sailor in the number "Always True to You in My Fashion".
The original Broadway production of "Kiss Me Kate" opened at the New Century Theater on Thursday, December 30th, 1948 and ran for 1077 performances. The show was the among the first recipients of the Antoinette Perry (Tony) Awards in 1949 for Best Musical, Best Book, and Best Musical Score.