Factual error: This episode happens on the first days of November 1935. During the 5th of November fireworks Hastings, Japp and Poirot walk at night through streets with plants prospering and in full green, and the same happens during the visit to the golf course.
Factual error: As Japp and his moustached pal visit the nightclub in search of Major Eustace, the song "Hindustan" is executed. While it is a song perfectly believable for the year (stated as being 1935) since it was written in 1918 and a huge hit, the version played here is quite a bit different, sounding a lot more like the upbeat version heard first in the Rosemary Clooney-Bing Crosby album "Fancy Meeting You Here", which had other classics reworked for the duet formula with added lyrics - exactly like in the back-and-forth heard here between the singer and the band. Said album came out in 1958, though. (00:30:20)
Continuity mistake: During the conversation with Laverton-West at the pool, in the close-ups of Poirot and Japp there are always two gentlemen chatting poolside near the bench where the politician dropped the towel. In wider shots, that's not always the case - plus, one of them walks away without a towel but he's back wearing it. (00:27:50 - 00:28:50)
Other mistake: Miss Lemon reminds Poirot of the dentist appointment he has at 11. Poirot then receives a phone call from Japp. It turns out during the investigation that the police broke into the apartment at 10:45. Considering that at least a preliminary examination needed to be made and at the time of the phone call Japp was in his office and Poirot was still comfortably having his tisane, everything leads to believe that the dentist appointment should have been later in the day (or the events at the Mews sooner). (00:03:30)
Audio problem: In an empty golf course, at such a close distance as shown, there's no way Miss Plenderlieth would not hear Hastings calling Poirot, who "lost another ball." (00:41:20)
Revealing mistake: Towards the end of the preliminary murder scene inspection, look at the victim in the last close-up, following the part when Poirot picks up paper from the basket. Specifically, the gun hand: the pinky finger of the supposedly dead person, after being too long in the unnatural position, trembles a little. (00:07:30)