Arthur Ferguson Jones (Edward G. Robinson) and Wilhelmina Clark (Jean Arthur) work at the same accounting firm. Jones turns out to look exactly like the notorious bank robber "Killer" Mannion (also Robinson) and is apprehended by the police. After his true identity is confirmed, the district attorney gives Jones a letter identifying him, so that he can avoid the same trouble in future. Jones becomes a local celebrity and, at the behest of his boss (Wallace Ford), begins ghost-writing Mannion's "autobiography", with good-natured but street-wise Wilhelmina voluntarily acting as his "talent agent" to see that he gets paid. Mannion decides to take advantage of his mild-mannered doppelgänger and, ultimately, leaving Jones "holding the bag" for Mannion's crimes. He kidnaps Wilhelmina, Jones' visiting aunt, and a few others, and takes them back to his hideout. He instructs Jones to make a large deposit for Mannion's mother's benefit at the First National Bank, where police detectives are expecting Mannion to make another robbery attempt. Fortunately for Jones, he forgets to bring the check and unwittingly leads the police back to Mannion's hideout. Upon his arrival, Jones is mistaken for Mannion by the waiting henchmen and quickly realizes that he is meant to be the fall guy. When Mannion returns unexpectedly, Jones orders the men to shoot Mannion. The police arrive in time to capture the rest of the gang. With Mannion dead, Jones collects a reward and takes a long-desired cruise to Shanghai with Wilhelmina.

Passengers on a ship traveling from Mexico to Europe in the 1930s represent society at large in that era. The crew is German, including the ship's Dr. Schumann, who falls in love with one of the passengers, La Condesa. A young American woman, Jenny, is traveling with the man she loves, David. Jenny is fascinated and puzzled by just who some of the other passengers are.

Sam Bowden witnesses a rape committed by Max Cady and testifies against him. When released after 8 years in prison, Cady begins stalking Bowden and his family but is always clever enough not to violate the law.

An ailing famous barrister agrees to defend a man in a sensational murder trial where his self-possessed wife's unconvincing testimony confuses him.