Minutes 5 - 6: Everyone in the group has a glass of champagne. Poirot puts an empty glass on the tray. After the waiter says "madam?" someone's un-gloved hand (from the left) picks up a champagne glass without putting one down. The woman is wearing gloves and Poirot is to the right. In the next shot, no one appears to be holding two glasses.
When the movie ends that Japp, Hastings and Poirot are watching, they (and most of the audience) leave immediately. When this show was set the national anthem was always played at the end of the movie and most people stood for it and didn't leave the cinema until it was over.
The Italian flag on the right on the Italian embassy is hanging upside down (with the crown on the coat of arms of the house of Savoy on the bottom, rather than on the top).
The movie that is being watched at the beginning is _G-men(1935)_. Later on the comment is made that Bonnie and Clyde were running around the American Mid-west. Bonnie and Clyde were killed May 23, 1934.
FBI Agent Burt vehemently denies the existence of any organized criminal society, whether calling itself The Mafia or The Cosa Nostra. This is set in the 1930s. The term "La Cosa Nostra" was unknown until October of 1963 when Joe Valachi revealed to Senator McClellan's Senate Crime Subcommittee that the Mafia did indeed exist and that its secret name was "La Cosa Nostra".
The man from America was said to be from the FBI, which name was adopted in 1935, but then they speak of Bonnie and Clyde being at large at the same time, and yet they were already dead in 1934.
When Ms Lemon goes to meet singer Elsa Hart, the manager tells her "Straight down the corridor, second on the left." She goes down the corridor, but the door she knocks on is the 2nd on the right.