Plot hole: Can't fault this massive plot hole to the adaptation, but to the source material; the culprit (forgetting the stupidity of writing an incriminating letter detailing the plan to murder someone, and put it in a desk he shares with her) since there are people outside the room that are about to enter, tears the letter in 3 neat vertical strips, rolls them, puts them in the vase on the mantlepiece, and then opens the side door to slip away...instead of simply pocketing the letter and going through that same door. Nobody was going to search him or anything and could have burned it, torn it into confetti, anything, later. It takes way way longer to do what he did, which needed him to stay there in the room increasing the chances of being found out. And of course he and his accomplice do not retrieve the letter after.
Continuity mistake: Poirot is holding up a letter in an envelope. He turns it to show the front to Lady Mayfield. The flap of the envelope appears to be tucked in. The shot cuts to a close-up, but now the back of the envelope is facing Lady Mayfield and the flap is sealed. He then turns the envelope to show her the front. (00:44:20)
Continuity mistake: When Poirot pulls out of the drill hidden in the handle, he holds it triumphantly in his right hand. In the next shot he mounts it on the handle starting the motion with the drill already in the left hand and the rest of the gimlet in the right. (00:40:00)
Factual error: Throughout the episode there are sections of dialogue in Greek, which are deliberately left untranslated. The subtitles frequently transcribe the Greek inaccurately. For example, the Greek girl who assists Poirot and Lyall in finding out about the poison says "Elate!" to them, which means "Come!" said to more than one person, but this is transcribed in the subtitles as "Ella!", the form used to a single person. Later on, the girl's grandmother says "Ohi enas Anglos anthras. Mia Anglitha yineka. San esena" ("Not an Englishman. An Englishwoman. Like you"), but this is given in the subtitles as "Ohi enas Anglos anthras, che yenika. Son ethena", which doesn't make sense. (00:40:45)
Factual error: At the end of the report on the findings of the crime scene, the "Italian" inspector tells to his subordinates what literally would translate as "Removes this meddler from here, no more access to the prisoner, that you understand?", which is just wrong in accent, cadence and construct. (00:36:30)
Deliberate mistake: The day of his scheduled departure, Poirot overhears conversations (mainly the one from the window of his room) he couldn't possibly be hearing given the long distance outdoors and the tone of voice. His reactions are shown as if he could hear and not simply see and infer the meaning. (00:23:00)
Revealing mistake: As the major tries to convince the Chief Inspector to leave the island, we see Hastings come down the stairs. However, prior to this we can see Hastings waiting just out of shot for his cue to enter. The edge of his hat is visible for several seconds, and when he's cued he begins walking into the shot. (01:15:27)
Plot hole: When Poirot and Hastings break into the house, they search the entire house for the box, without success. However, later on, when they are in the kitchen, the housekeeper comes down the stairs - having been lying in wait for them. How did Poirot not run into her when he was initially searching upstairs, particularly when he was making such a thorough search?
Plot hole: Since the Countess was the only person to be at every dinner when the jewelry thief was in action, it takes a very special kind of idiot to not identify her as the culprit. Japp here did not need at all Poirot's acumen, but simple due diligence cross-checking the guest lists, something there is absolutely no reason he wouldn't do, and yet she is never treated as a special suspect. Also, Japp's job is described as being in jeopardy after the first 3 thefts, a 4th happens, he does not quite solve it (but retrieves at least the necklace), but he's off the hook despite the thief being unidentified, at large and with still the jewelry stolen from the first 3.
Factual error: It is well established that the episode takes place in 1935 (Nairobi Daily Press dated Saturday July 27 1935, the poster in town advertises the meeting for "Today, Wednesday September 4th", day of the week consistent with the year), but Poirot and Hastings are stopped on their way to the train station by a Wolseley Series II - 14/56, a model that entered production in mid 1936. (00:17:00)
Factual error: At the party, Marcus Hardman tells Bernard that the Countess recently arrived from Russia, and she describes herself as being in exile. Which made sense in the source material, set right after the Russian Revolution, but less sense in this adaptation, set in the mid 1930s. If she stayed in Russia that long, she would have spent 15-20 years with zero privileges from her rank at that point, and nothing from her old wealth, seized by the communist government.
Other mistake: Investigating Poirot's investigation, the clumsy constable crushes a tiny egg under his foot. Poirot crawls to him and points with his cane at the other eggs in the bush. But he points practically at his shoe, and the eggs are in a different spot to the left. (00:20:10)
Plot hole: The murderer is in possession of chloroform from the doctor's cabinet, but there's no realistic timeframe when they could have done it, nor any explanation why the doctor notices it completely at random when Poirot visits, just approaching the medicine cabinet, something he routinely opens and looks through during the day.
Continuity mistake: The Countess arrives at the hotel at the beginning of the episode. In the overhead shot she reaches the top of the stairs with nobody close to her, just the porters behind her, but in the next shot there are other people in the lobby, who at the next cut are even closer to her to fit in frame. (00:02:10)