The Adventure of the Cheap Flat - S2-E7
Plot hole: The professional hitman from the US does not have a gun of his own, and does not bother in the long time elapsed between the apartment's hit and the nightclub (it could even be hours) to check if the gun he just grabbed is loaded or not. Who in the world would not take a split second of his time to peek at the cylinder and see how many bullets does he have? An assassin planning to kill with that gun, even.
The Adventure of the Cheap Flat - S2-E7
Factual error: Agent Burt brushes off Poirot's question saying "When will you guys understand there is no such thing as the Mafia, the Black Hand or the Cosa Nostra?" The last term he uses, while not impossible (since members of the organization were indeed referring to it as such) is a huge improbability, considering that officially FBI (and certainly the general public Burt is lashing at) came to know the real name (adapted in "La cosa nostra") only decades later with the Valachi investigations. (00:24:05)
The Adventure of the Cheap Flat - S2-E7
Factual error: When Poirot asks O'Brian about unsolved crimes with young couples as suspects, he says "There's that Bonnie and Clyde of course, but they're at large somewhere in the American Midwest", to which Poirot replies "And let us hope that is where they remain." Bonnie and Clyde were killed in Louisiana on May 23, 1934. The episode is set in October 1935. (00:12:20)
The Adventure of the Cheap Flat - S2-E7
Continuity mistake: During the party, the establishing shot shows everyone in the small circle Poirot is a part of having a glass of champagne. That includes Mr. Robinson. As Poirot puts on the tray his own glass, someone's hand reaches over for another - it can only be Mr. Robinson's, as his wife is wearing gloves, but he never put down his own glass. (00:06:05)
The Adventure of the Cheap Flat - S2-E7
Continuity mistake: Hastings, Japp (for some reason) and Poirot are at the movies; when the camera pans through the room, there's a guy sitting behind Hastings, while behind Poirot there are a red haired woman and a man, as confirmed by the close-ups. When the music stops and Hastings tells Poirot that he can open his eyes, the couple have moved behind Hastings. (00:02:50)
The Adventure of the Cheap Flat - S2-E7
Continuity mistake: In the first scene with the 'G-Man', the room in the shots with the camera roughly by his shoulder is lit in a different way, with his body fully in the 'sun'. Especially visible when he picks up the phone and starts spouting yankee-isms going all "Yeah yeah so what yeah." (00:09:00)
The Adventure of the Cheap Flat - S2-E7
Continuity mistake: Miss Lemon, as Penelope Maitland, enters the performer's room. The shady character that opens the door does it holding a cigarette in his left hand. The hand is kept close to his chest in one shot, while it's on the door in the reverse. (00:31:35)
The Adventure of the Cheap Flat - S2-E7
Continuity mistake: Poirot is doing his round of phone calls at night clubs looking for the chanteuse; the pen before Hastings' arrival is pointed to the left side of the screen, when he sits down (and Poirot has not touched it) it points to the right. (00:24:40)
The Adventure of the Cheap Flat - S2-E7
Other mistake: Spying on the Italian embassy from Japp's van, the building has 2 Italian flags of the period. But the rightmost one is mounted upside down, with the crown under the shield instead of the opposite. (00:23:05)
The Adventure of the Cheap Flat - S2-E7
Character mistake: Bernie Cole "King of the clubs" greets Miss Lemon and tells her she'll find Elsa "Straight down the corridor, second on the left." So she opens the second door...on the right. And it's the correct one. (00:30:50)
The Adventure of the Cheap Flat - S2-E7
Continuity mistake: Poirot knocks at the door of The Black Cat, next to a street worker and a pimp. Nobody is walking down the street in the wider shot, but in the close-up an elderly couple passes by. (00:22:55)