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.
Continuity mistake: During the sentence when Hastings tells Poirot he's got "No imagination at all", the lady sitting behind the Belgian faces the other way between shots. (00:02:25)
Factual error: Nick says that she made the will 6 months before the events of the episode, just before her appendix surgery. The surgery happened on February 27th, so it would be the end of August now. But at the beginning of the first episode Hastings was reading a (movie prop) copy of the Daily Express which had on the cover "Perry makes a new record - Champion two years in succession", complete with a picture where he is unmistakably with his rival Gottfried Von Cramm. The photo (and the mention of the 2 years record) is about the Wimbledon final who took place on 5 July 1935. That's almost 2 months earlier than it should be. (00:04:45)
Factual error: Poirot has just suffered "a turned ankle", in his words; he's talking with Hastings and the kind woman who helped him out, when their conversation gets perturbed by the noise of a plane. Which is surprising, since the plane in question is a Volmer VJ .22 Sportsman, a plane from the 50s, way after the 1930s setting of the episodes. (00:06:40)
Audio problem: Nick gets supposedly grazed by a bullet fired while the plane's noise has already diminished considerably, making quite unlikely that any gunshot could be drowned out by it. (00:06:50)
Continuity mistake: Poirot shows Hastings Nicki's hat; he holds it in a different way (using the thumb to pinch, or with the light brim tucked in between index and middle) between shots. (00:08:55)
Continuity mistake: Poirot and Hastings are eating after their first visit to End House. During the entire scene, natural light changes in intensity depending on the angle of filming. (00:20:15 - 00:21:10)
Continuity mistake: When Poirot shows Freddie the bullet, in the close-up his hand is right by the sugar bowl, but he was shown putting the cigarette holder at greater distance, closer to Freddie herself. (00:25:05)
Continuity mistake: When Mr. Vyse is beginning to talk about the new will, in the wide shot encompassing the whole table, the open folder is raised, as the left page is sitting on top of another object. In the close-up of the letter, the folder is perfectly level with the table. (00:34:45)
Plot hole: The whole premise of the plot is that nobody is staying at End House but Nick (and the servants); she even says explicitly that there is just one room that is usable and everyone else stays at the Majestic. During the party though, Freddie tells Maggie to go get her coat which is "in my room." They are at End House, not the hotel, how would Maggie have a room there? (00:35:00)
Continuity mistake: Once Ghost Nick enters the room and Poirot turns on the lights, the Crofts stare at her, and you can see in frame the right arm of "Mne LeMon", sitting by Milly. Next shot though, Miss Lemon is standing on her feet. (00:40:10)
Continuity mistake: Poirot rudely awakens Hastings with his three questions. You get a good view of Hastings' wristwatch on the bedstand. When at the end of the Q&A Hastings turns his attention to the watch, it is in a completely different position. (00:41:25 - 00:42:35)
Continuity mistake: When Freddie holds the Mauser 1910 gun, Alison Sterling holds it in a very characteristic way (thumb and and pinky finger stick out) in the front views. It is held in a much more orthodox way in the views from behind. (00:43:50)
Continuity mistake: Poirot and Hastings are talking with Freddie, by her invitation. She says "You'll be giving me a diploma next" and three extras walk by her chair. In the following shot she completes the action of standing up, but the extras are still there, behind their original positions. (00:44:15)
Factual error: Jim Lazarus drives a Vauxhall DX (14/6 Light Six) Stratford Tourer, a 1936 model. This episode takes place in the summer of 1935. (00:46:20)
Continuity mistake: Jim Lazarus pulls over by the protagonists to complain about being unable to see Nick. During the scene, Paul Geoffrey's different facial expressions are shown in the side mirror of the car, but each time we cut back to him, he has the same stoic face listening to Poirot. (00:47:00)
Continuity mistake: Miss Lemon's ice cream quite literally melts between shots (and the actress ignores the dripping on her fingers). (00:51:15)