According to Sir Roger Moore, Lee J. Cobb had a heart attack while making the film, and was hospitalized. Frank Sinatra called Cobb at the hospital, and said, "Kid, don't worry about the bills", and proceeded to pay for his medical expenses.
During an on-set interview, Lee J. Cobb said about his appearing in this picture in an article published in the May 1975 edition of Photoplay (UK) magazine: "Someone slipped, obviously. But I'm glad they asked me. I'm enjoying it. Actually, I love playing comedy. That I'm a low comic at heart, is one of the best kept secrets in the world."
Producer Dimitri De Grunwald said of this movie in its press publicity: "Our film has one object, and that is to entertain. We aim to make That Lucky Touch (1975) a comedy of style and sophistication, a fun picture for a world audience".
One of this film's main movie posters is designed in painted artwork, featuring Sir Roger Moore standing in a James Bond-like pose, wearing a bow tie with a blue, black, and white tuxedo, positioned next to two women, with a gigantic casino golden colored roulette wheel, situated behind the three characters.