Character mistake: In the hotel lobby, Poirot, indignant of Hastings' attitude towards the murder case, says "After three attempts had been made at the life of M. Nick, Poirot gave his word he would protect her." But he did that after four attempts; Nick already avoided 3 "mysterious accidents" (painting, car, boulder) and Poirot witnessed the 4th, the bullet that pulled him into the whole case to begin with. (01:02:20)
Character mistake: The rude doctor says that Edward Pengelley "wouldn't poison his grandmother's dog", to which Poirot irately blurts out "but it is not the dog of Madame Pengelley's grandmother that has been poisoned." He should have said "of Monsieur Pengelley." (00:12:50)
The Disappearance of Mr. Davenheim - S2-E5
Character mistake: The magician's assistant wears a costume that leaves her legs exposed, and the costume itself vanishes. The trick can't go as Poirot describes to Hastings and Japp (and it is made with a TV editing trick). (00:07:05)
The Adventure of the Cheap Flat - S2-E7
Character mistake: Bernie Cole "King of the clubs" greets Miss Lemon and tells her she'll find Elsa "Straight down the corridor, second on the left." So she opens the second door...on the right. And it's the correct one. (00:30:50)
The Adventure of the Western Star - S2-E9
Character mistake: While handing Mademoiselle Marvelle's letters to Hastings, Poirot calls him "Chief Inspector". (00:06:55)