The film was unavailable for decades because its rights (together with four other pictures of the same period) were bought back by Alfred Hitchcock and left as part of his legacy to his daughter. They've been known for long as the infamous "Five lost Hitchcocks" amongst film buffs, and were re-released in theatres around 1984 after a 30-year absence. The others are Rear Window, Rope, The Trouble with Harry, and Vertigo.
The movie was originally to be produced by Paramount Pictures and Patron, a company to be jointly owned by James Stewart, Doris Day and Alfred Hitchcock. When the film finally went before the cameras, the production company was Filwite Productions, Inc., co-owned by Hitchcock and Stewart. The reason Day was not included in the final production deal has not been publicly disclosed. However, it may have had something to do with Day's husband and manager at the time, Martin Melcher, a man absolutely despised and considered shady by many in Hollywood.
The plot calls for a man (Daniel Gélin in the role of Louis Bernard) to be discovered as "not Moroccan" because he was wearing black makeup. The makeup artists couldn't find a black substance that would come off easily, and so they painted the fingers of the other man (James Stewart) white, so that he would leave pale streaks on the other man's skin (according to Patricia Hitchcock, this idea was suggested by Daniel Gélin).
Throughout the filming, Doris Day became increasingly concerned that Alfred Hitchcock paid more attention to camera setups, lighting and technical matters than he did to her performance. Convinced that he was displeased with her work, she finally confronted him. His reply was, "My dear Miss Day, if you weren't giving me what I wanted, *then* I would have to direct you!"
When Doris Day traveled to London to film some of the location scenes for this film, she was so popular with the British that when she arrived at her hotel, mobs of fans who had gotten word that she would be staying there had gathered. Pandemonium erupted when they saw her, and she needed a police escort to get in. Fans continued to surround the hotel, camping out, shouting her name, asking for autographs and hoping for a chance to see her. The hotel management finally had to ask her to leave.