Although great pains were used to disguise the name of the country in the film, Dr. Ferguson mentions that President Farrago should go to a neurological hospital (which he mentions is just across the border) in Chile--which narrows the country down to either Argentina, Bolivia or Peru. Other hints include: Peso/Dollar law, the blankets worn on the train, license plates on vehicles.
The South American dictator, Farrago, and his beautiful wife seem clearly modeled on Argentine dictator Gen. Juan Domingo Perón and his wife Eva Perón--something writer-director Richard Brooks conceded in a 1965 interview.
Directorial debut of Richard Brooks. NOTE: Brooks was at the Santa Anita race track where he met Cary Grant and struck up a conversation about this film; Brooks wrote the story but also wanted to direct; however, none of the studios would let him. Grant asked for a copy of the script and loved it, so much so that he went to MGM and said he would love to do the movie but only if Brooks was the director.
The original story was about the doctor's daughter getting kidnapped and there was no wife. However, once MGM had Cary Grant cast it insisted on a re-write so that Grant would have a love interest.
The sport played at the very beginning of the film, which may be foreign to modern audiences, is Jai Alai. During the first half of the twentieth century, Jai Alai was a very popular sport in Latin America, South America, and Europe. Betting on the games was a common cultural activity. In Argentina (which the writer/director admitted was the inspiration for the country in the film), most Jai Alai courts (or frontones) were closed following Peron's revolution.