Continuity mistake: Ginevra just left because her mother sent her to bed. Jefferson Cope approaches Nadine. Look at the lady sitting at right of the table behind the Boyntons. Right arm on the table, left arm on the chair. Cope brazenly asks Nadine's husband if he doesn't mind, and both her hands are on the table. (00:15:45)
Factual error: After Lady Westholme commented on Poirot's absence, and we saw him seasick in his cabin, the focus is again on the Boyntons. In the background you can see the ship's other guests entertaining themselves with a dance. They are dancing to the tunes of a rearranged version of "Ta-Ra-Ra Boom-De-Ay", which is perfect for the time period, but their dance is a version of the "Lambeth Walk." The movie takes place in May 1937, and the musical "Me and my girl" that invented and popularized this dance would debut in December of the same year. (00:15:10)
Continuity mistake: Lady Westholme asks her travel partner Miss Quinton "What's the matter" since she keeps rummagining inside the bag. It's an instantaneous exchange, but between shots the couple of passersby (man with a suit and red flower, woman with an azure dress) have advanced through the street by a great deal. (00:10:45)
Continuity mistake: When Ginny tells the others that Cope is in Trieste, the couple in the background changes position and the woman and the man switch places. (00:09:25)
Continuity mistake: The Boyntons are in Venice and looking at the Rialto bridge. Ginevra in the wider view of the staircase puts her hand down from the railing, and the hand is back up on it in the next. (00:07:50)
Continuity mistake: When Carbury mentions Wallis Simpson to Lady Westholme, he's holding his baton alternating an overhand grip with an underhand one. (01:26:40)
Audio problem: Hassan runs away, chased by Dr. King. A wild Lady Westholme appears and says a line that does not match her lips. (Peter Ustinov's lips move without a sound as well, but in his case Poirot is self-censoring an expletive). (01:15:15)
Revealing mistake: When Poirot reads the newspaper detailing Lady Westholme's death, the font and the clarity of the print on the article stick out from the rest of the page like a sore thumb. (01:38:30)
Continuity mistake: Just before Poirot moves to the other side of the dinner table after revealing lady Westholme's deception, Dr. King at first has both hands on the table, but in the next shot she is in a different position. Same for Jefferson Cope and his cigarette; he's smoking, then he is not. (01:33:55)
Plot hole: Dr. King is chasing Hassan through the market. She runs after him at great speed; even assuming that they could have run in a circle for a while, it makes no sense (especially given her role in the plot) that Lady Westholme is one of the people in the market crowd, casually chatting with a merchant, when she was behind Poirot, at the hotel, as the chase started. (01:15:45)
Other mistake: Lady Westholme leaves the room to take a call from England from her husband, Lord Westholme. When she gets back to Poirot, she mentions with outrage the call from Colonel Carbury. It can't be both, it's not even where she lives or works.
Continuity mistake: Lady Westholme is cross with Poirot and making her exit from the office she leaves her leather folder behind. Look at its position on the table; Miss Quinton fetches the bag on her way out, and it is placed differently, as made evident by the way it sticks out of the table. (00:58:35)
Audio problem: Lady Westholme pushes the half-open door against Poirot twice. The door makes the same sound it does when it gets slammed shut later (twice). As stocky as Peter Ustinov is, he's not made of wood, and while obviously a door hitting a person would make a thud (I admit having tested it), it wouldn't make the kind of sound heard here. (00:58:35)
Other mistake: Poirot enters the office of the Royal Commission at 10 to 11. We see and hear the interactions between him and the other people, and barely five minutes pass, but the clock is a minute past 11 when Lady Westholme comes back. (00:53:00 - 00:58:00)
Continuity mistake: Poirot is with Lady Westholme and Miss Quinton at the Royal Commission. A man from the staff opens the door, and Miss Quinton turns all the way to look. He announces a phone call, and the reaction shot on the ladies begins with the woman turning around again. (00:56:25)
Continuity mistake: In Lady Westholme's flashback, she asks Emily if there's anything she and Miss Quinton can do. From the front, the table and the woman's lap are in the shade, but in the reverse shot they are fully sunlit, and back with no sun when she watches them leave. (00:56:00)
Continuity mistake: Inside Lord Peel's study, Poirot asks Lady Westholme what did she do after lunch, since "You did not immediately go for your walk, I believe." Peter Ustinov poses the question with his hands behind his back, but Lauren Bacall's answer answers with the stand-in for Ustinov posing with his hand on his hip. (00:54:40)
Continuity mistake: When Ray tells lady Westholme that his mother would like a word with her, the position of the folders in her hands change. (00:41:40)
Audio problem: During the fireworks, Poirot's line about the "nice and royal" show giving him "confidence" is dubbed over, and you can in fact see Peter Ustinov in the shot of the crowd, not saying those words. (01:37:40)
Audio problem: When Poirot stands from his seat after telling the truth about the spider, he looks at Dr. King. Her lips move but there is no audio. (01:33:50)