Continuity mistake: When Jimmy reads the solicitor's letter, the date is 5 October 1935. Hastings wrecks his car here but in Murder in the Mews, taking place on the 6th of November, he has it again. Assuming that he has been able to get his car back to form entirely restoring/replacing the ruined sections (Japp tells him that it's now just "an expensive scrap of metal"), in that episode the car needed ordinary maintenance work, while going by the events of this episode it would have been fresh off the car shop instead.
Character mistake: As Poirot reconstructs the facts in the flat (and he explicitly says "consider the FACTS"), he lays out that "a letter which was found at the scene of the crime with John Frazer written on the bottom." But the letter simply said "Frazer", the first name was just Japp's random conjecture based on the initials on another evidence being J.F. (00:27:40)
Continuity mistake: As Poirot stands from the late dinner with the young socialites to go talk to Inspector Japp next to the door, he leaves his napkin on the table. The napkin changes between shots, going from mostly straight to crumpled (when Mildred says "How dreadful!") to straight again. (00:22:20)
Continuity mistake: As the two porters are carrying the piece of furniture, the draping on top of it goes all the way down one side when they have just unloaded it from the van, and the opposite side when they are bringing it up Whitehaven Mansions' stairs getting cranky at the doorman. (00:01:40)
Continuity mistake: During the entirety of the scene in the kitchen, Patricia keeps her hands in her lap, but they change repeatedly from being side to side, to her right hand lying on top of the upturned left. (00:22:40)
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)
Character mistake: Somehow, Poirot is the first person to get to the basement - he obviously would have slowed down terribly the policeman and the young and spry Jimmy rushing down the stairs with him.
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.
Continuity mistake: Once Poirot hypothesises that the lightbulb could have been replaced, he curls back his finger pointed at the young fellas. New shot, and he is back pointing fingers. (00:18:45)
Answer: He definitely says "Belgian", but the subtitles get it wrong and show him saying "American."
Wblank71