As the following tanks begin to go down the steep embankment, a few of them can be seen rolling over; but when the shot changes to the bottom of the hill, all the tanks are right side up and in line.
While Thompson is drinking his hangover cure with his new secretary, in one cut a bottle suddenly appears in his hand that was not there the shot before.
According to the date on the article Mac types about the assassination attempt, the action in the film takes place in late June. When they arrive in New York it couldn't be later than July, yet an article lower on the same front page as the headline detailing their adventure is about the final game of the Brooklyn Dodgers' baseball season, which wouldn't be until October. However, in reality the last game of the 1940 season saw the Dodgers defeat the Phillies in Philadelphia on 29 September. They won 5-0. At the time, the Dodgers were 12 games behind Cincinnati. The last time they played the "Reds" was on 16 September at Ebbets Field. The Dodgers lost that one 3-4. Brooklyn's 1940 ended at 88-65-3 (yes, they still had tie ballgames). Brooklyn did go to the 1941 World Series, losing it to the Yankees.
The railroad cars in the railroad yard are distinctly American design.
The script makes reference to the Soviet law that a person could divorce his or her spouse simply by sending them a postcard announcing that the marriage was over. But in 1936, four years before this film was made, Stalin had repealed that law when he rewrote the Russian constitution and made divorces considerably harder to get.
When McKinley Thompson goes to check into the hotel, he insists he is the rightful tenant of room 301. Later, in the room, he calls room service and says he is in room 310.
Near the end, the leader of the Soviet tanks gives them an order to turn right (in Russian), but they all are shown turning left.