Character mistake: When they are having the going away party for Paul, "leisure" is spelled wrong on the cake.
Character mistake: The story arc set on the Mole covers one week. The Highlanders attempt to refloat the beached trawler on the last day of that week. One of them confidently states that the tides are three-hourly. (The audience know this isn't true because we've seen a similar conversation between the Admiral and the Colonel.) At least some - if not all - of those Tommies have been on the beach all week. Have none of them have noticed that the tides are six-hourly?
Character mistake: It is highly unlikely that the recipient of Mr. Butler's application for the professorship position would not only call him so soon, but ask him to come to her office right away (where she would humiliate him for the things he wrote in his essay on "qualities that make me a good teacher"). Moreover, her failure to listen to Mr. Butler and give due consideration to his assertion that someone else actually wrote those offensive things showed poor judgment, especially since she knew the person who referred Mr. Butler and spoke highly of him. Someone tampering with his application would make more sense than believing that Mr. Butler actually wrote those things that criticized the very college he was applying to and boasted so much about himself. That Mr. Butler was not able to say more to make his point believable is also problematic. He is an English teacher, so should have the vocabulary and mastering of techniques to make a convincing argument, but he failed to defend himself.
Character mistake: Poirot identifies Prof. Hardman's revolver as a 1927 police-issue weapon due to its blued finish and chequered grips. In fact, these features were common in the widely-available civilian versions of the Colt 'Police Positive' revolver and not the least bit specific to police-issue weapons.
Character mistake: King George VI got out of car in admiral's uniform without his cap and saluted another officer. RN officers do not salute without their caps.
Character mistake: When Joan and Joe are first alone in their suite in Stockholm, Joe tells her he wasn't attracted to a woman. Joan says, "I could care less." There's no way a college-educated writer (married to a Nobel laureate in literature) would use that phrase. The correct phrase is "I couldn't care less."
Character mistake: Henry believed his call to the Saratoga County Help Line #1-518-555-0121 was not effective because Glenn's brother George was the Social Services Director. The genius failed to look above the county level and discover there's a STATEWIDE CPS number that he could have turned to #1-800-342-3720. A call to the State CPS hotline probably refers calls to the relevant county, but Henry could have used what he wrote in his notebook "Why Calling Child Protective Services is not a plausible option." (00:28:56 - 01:01:11)
Suggested correction: It isn't clear what number Henry called. He had the county number underlined on the brochure, so I assumed that was the number he called. However, I replayed that part and the person who answered said "Child Protective Services." There was another number above for "National Help Line for Victim Advocacy" 1-800-555-0199, but that's not the National Child Abuse Hotline.