Continuity mistake: The story as presented would be impossible. In the story, Poirot tells his audience that the victim was dead at a time which is earlier than the time that he later tells his audience the victim was killed. (00:37:00 - 00:44:00)
Plot hole: Nobody hears the sound of a gun being fired past a door they were waiting almost in front of, and the police cannot tell apart a shot fired point blank by one fired 20 feet away and probably at a very sharp angle. Moreover, the bleeding should be all over his face, since leaning the way it is shown in this adaptation is most likely to lead the victim to fall over, and even leave bloodstains out of the window and on the ground below, which someone would have noticed in the crowded factory.
Other mistake: This adaptation opens with a nice fake Pathe Gazette news reel. The voice says that "last year" Farley sold a record 5 million pies, and that the new wing of the plant is due to open. At the inauguration, there's a banner behind him saying "1885-1935" and he's saying that in 1935 they sold more pies than at any point in their history, and he gives the kind of speech you give at the beginning of a year, trying to set a new record while still on the hot trail of the previous. At the same time, Miss Lemon tells Hastings that the typewriter broke 'last Easter' and she burst out with Poirot that she has been complaining 'for the last six months', which would put the event at the end of the year.
Other mistake: At the end of the episode, the clock Poirot presents to Miss Lemon is pointed exactly at 3:28, which would be the time of the murder in the original novel, not in this adaption, when it was changed to 12:28.
