Other mistake: When Hastings pulls Poirot's slip of paper out of his pocket, he's reading it upside down - as you can see from the close-up, the torn up part should be at the bottom, not at the top. (00:11:40)
Other mistake: At the very end of the episode, Miss Lemon stops talking as if she could see Poirot glaring at her above the newspaper - while in fact, he is facing the other way.