A title card immediately after the opening credits states the movie takes place in 1933. In a radio broadcast played during the opening credits when Arno is on his boat, the radio announcer says the date is Saturday, September 12. September 12, 1933 is actually a Tuesday.
When Arno escapes in his boat during the storm, the men shooting at him use the two-handed grip on their pistols. But this technique was unknown at the time. It was first developed by Jeff Cooper in the 1950s.
At the end of the movie, the bartender gives Arno a package. He opens it, finds his watch, asks what time it is, and then says, "She fixed it," implying that it is running and showing the right time. But it is an old-style pocket watch which needs regular winding, and the bartender said she hadn't seen him for a long time, so it couldn't possibly still be running.