Continuity mistake: The only letter that Alexander B. Cust really wrote himself is briefly shown when Poirot visits the office of the Twinkle Toes stocking company. The lowercase "R" is too high every time (meaning that the typewriter isn't perfect, a detail put in for realism). Yet all the close-ups of a typewriter progressing through the work on that letter, or any of the letters written on the same machine, show a perfectly aligned "r."
Episode #1.3 - S1-E3
Continuity mistake: Poirot is talking to the owner of Twinkle Toes and confirms that indeed the victim was strangled with his merchandise. The man listens with his fingertips adjoined and pointed towards Poirot, but when it cuts to his response ("Poor kid") his left hand is partially in frame and in a different position altogether. (00:17:50)