The Kidnapped Prime Minister - S2-E8
Continuity mistake: When Poirot tells his tailor that it's his equipment that is at fault, Hastings holds the newspaper in ways not coherent between shots (he folds it, but in the reverse shot is still looking at the top of the page, and so on). (00:04:20)
The Kidnapped Prime Minister - S2-E8
Factual error: The Austin used by Poirot and his company to go to the attempted murder scene and back is an Austin 18, which entered production in 1937, later than the event of this season/episode. (00:12:00)
The Kidnapped Prime Minister - S2-E8
Continuity mistake: Poirot opens the car window in two shots; in the first he is holding his walking stick close to the body, but in the second he has a completely different posture, with the cane perfectly vertical and his arm at a right angle. (00:13:20)
The Kidnapped Prime Minister - S2-E8
Continuity mistake: At Scotland Yard, Poirot is readying the glasses for the moment when Japp will pass him the paper he's reading, about the driver. When the view switches, his hands, that were above the desk level, start off from underneath the desk. (00:33:35)
The Kidnapped Prime Minister - S2-E8
Factual error: The calendar behind Japp in Scotland Yard places November 13 as a Tuesday, but that is wrong for 1935, when the story is set (the whole season consistently goes with 1935 historical facts, Poirot in this episode makes a reference to "the Dutch", and the newspaper page Hastings shows up with at the end of the episode talks about the notorious gangster's death, happened that year). It was a Wednesday in 1935, to be Tuesday it should have been 1934. (00:34:00)
The Kidnapped Prime Minister - S2-E8
Factual error: When the former Mrs. Daniels hops on her car followed by Hastings, between them you can see a speed bump, not a feature on roads in Britain (or anywhere) at the time. (00:36:55)
The Kidnapped Prime Minister - S2-E8
Continuity mistake: Hastings has lost sight of the car he was pursuing, and stops at the crossroads. In the wide shot you can see his left hand holding the top of the windshield, but in the close-up he's using just his right hand. (00:40:40)
The Kidnapped Prime Minister - S2-E8
Factual error: At the end of the episode, during the fitting of the jacket with monsieur Fingler (last role of character actor Milo Sperber), Hastings is reading a newspaper prop sporting a doctored first page (the real headline, which was about Italy, is replaced by the fake PM speech) of The Daily Express based on the real Friday October 25th, 1935, which is wrong in month and day of the week (the appointment was on Thursday and it's supposed to be November going by the various calendars seen throughout the episode). (00:51:00)
The Kidnapped Prime Minister - S2-E8
Factual error: Poirot in this episode has to save the Prime Minister, kidnapped before he could attend the League of Nations Disarmament Conference. This episode is set in November (the previous of the season in October), but it can't possibly be 1935, since the Disarmament conference happened between 1932 and 1934. It makes mention of the PM being vital to have at least a chance at preventing Germany's rearmament, with Hitler withdrawing Germany from conference and League of Nations entirely in October 1933. It should be noted though that the conference happened in Geneva and not in Paris like it's described here. The original material did not have this sort of inconsistency since it was set to happen much earlier in the century and for the Treaty of Versailles, where Paris would have been the correct destination. Both short story and adaptation have as prime minister a fictional "David MacAdam", with him designed to be a stand-in for David Lloyd George, just recently replaced as PM.