Factual error: The building shown between the stated times is located in Japan instead of the US/Washington DC as suggested by the actions in the scene. This is proven by by the Chinese characters In the Dark-gray concrete wall in the lower left side of the frame, as well as the red and blue colored circular road signs in the lower far right of the frame which are not in use in the US but in this combination unique to Japan. The street furniture, such as the road markings, the vegetation and the buildings also resemble Tokyo. (00:06:55)
Factual error: The show starts in 1901 with a woman constable working for the Metropolitan Police Service (Scotland Yard). However women didn't join the Metropolitan Police until 1919 (which is also when the first woman's police uniform was created). Prior to that, women volunteered in the Women's Police Service, but that wasn't formed until 1914.
Factual error: Ray, Sara, and Kendra are Left Behind in 1958. However, 10 weeks later Sara and Kendra are playing the board game "The Game of Life." The modern version, as seen, didn't come out until 1960 (previously it was called The Checkered Game of Life and doesn't resemble the modern version).
Factual error: When Riggs and Murtaugh go to investigate the scene where the body of Ramon Alvarez is discovered Scorsese states that Alvarez's dog tags say "SEAL" on them. His dog tags would not say that he is a SEAL on them. The information listed on dog tags is as follows: Name, Social Security Number, Blood Type, Service Branch, and Religious Preference. There is no way to tell what a given service member's MOS (job) from his or her dog tags. (00:14:00)
Factual error: With two exceptions, all the policemen shown in both 1949 and 1953 are wearing the old-fashioned tunics with high, closed collars. The Metropolitan Police adopted the more modern open-necked tunic with collar and tie in 1948, and this is shown worn by the policeman who visits Christie and by the officer who arrests him.
Factual error: Bozer and for that matter I would assume all of the team went to a spycraft academy. A basic subject in any of such academies is surveillance, including proper techniques to follow and stake out someone. Bozer being so inept at tracking MacGyver's father is inconceivable given their training.
Factual error: "Underground" is set in 1857 Georgia, yet the padded baseball glove August Pullman gives to his son is of a type used during the early 20th century. Before 1883 when padded gloves were first manufactured, gloves were either not used by baseball players or railroad brakeman's gloves were used.
Factual error: Once the Queen has given Mr. Churchill his "dressing down", he simply turns to leave the room. However, he had not been dismissed. The Queen always pushes a button positioned on a side table to call her equerry who enters the room to escort guests out. With Mr. Churchill, she did not request her equerry. (00:54:00)
Factual error: When they're traveling to the farm to rescue her friend, (when a drone is filming from above following the truck down the road) there is light snow on the ground. Throughout the series in different parts, when they speak they're blowing mist/fog from it being cold. It isn't cold, snowing or any fall leaves in Mexico. Nor do those things hardly ever occur in southern Texas either.
Factual error: Randall flies out last minute across the country to Los Angeles to be at his sister's side for her surgery. The scene where he arrives at the hospital and meets up with her husband Toby in The Waiting Room is prefaced by an exterior shot of the supposed hospital building. The sign outside the hospital indicates the name as "Sutter Health Alta Bates Summit Medical Center," which is a hospital in Berkeley - the San Francisco Bay Area - about 400 miles north of Los Angeles. (00:19:30)