Continuity mistake: John Paul Getty approaches the kidnapper's cars and Getty removes his sunglasses and tucks them into his coat pocket. The next shot shows him still wearing them as the kidnappers approach.
Episode #1.1 - S1-E1
Continuity mistake: When David meets the Home Secretary for the first time outside her car, he is wearing a grey shirt. In the next scene (in the lobby) his shirt is white, before turning grey again later.
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)
Continuity mistake: At breakfast the apple being cut for Camille as she poses a question to Adora is suddenly on her plate as the scene cuts to Adora's immediate reaction. (00:05:07)
Continuity mistake: Ruth Deaver is helping Alan Pangborn put on his tie. The camera is facing Ruth's back and we see Alan's face in the mirror. The camera then switches angles to face Alan's back and Ruth's face. Alan's collar which was popped straight up from the first angle is now perfectly down over his newly tied tie from the second angle. (00:24:55)
Episode #1.6 - S1-E6
Continuity mistake: The paramedics zip up a red body bag containing Helen, who was killed in the fire. But they wheel out a black body bag a few minutes later.