Other mistake: Right at the start, as they're crashing, the computer narrates their rapidly-dropping altitude in feet. But the "altitude" dial we're shown is in metres. Most noticeable as they cross the 3,000 mark, when the computer voice and the height say/show the same number at the same time, despite the different units. 3,000m would be more like 9,000 feet, or 3,000 feet would be more like 1,000m. (00:03:20)
Factual error: A thief has stolen 75 million dollars. He runs out with two large duffel bags. All US bills weigh a single gram. This means that $1,000,000 in $100 bills - the largest bills in circulation - weigh around 10 kilograms, or a little over 22 pounds. $75 million would be 1,650 pounds. No way this could be carried in two duffel bags.
Other mistake: Episodes 4 and 5 of season 1 aired noticeably out of order. In episode 4, "The Nanny," Alex's former Nanny, Rosalba, comes to work at his podcast company, and its name, "Ajana," is mentioned a few times. But episode 5, "The Mother-in-Law," starts with the company unnamed; over the course of the episode, Alex learns of the concept of "ajana," the unknown, from his mother-in-law and chooses it as his company's name.
Plot hole: The FBI is looking for a "very tall" guy who has been identified as such by various witnesses and by their own expert due to the entry angle of a fatal bullet wound - 6'5" at least. They send Elena into a bar near the end of the show to meet the Albanian perp who when he arrives is barely average height.
Factual error: The American flag shown waving outside the White House is the current present-day flag with 50 stars. From 1896 to 1908, (the time period that this show is set in) the US flag only had 45 stars as Oklahoma, New Mexico, Nebraska, Alaska and Hawaii were not recognised as states in that time period. The flag did not have 50 stars until 1960. (00:04:30)
Factual error: This is set in 1933. When the killer comes back to his lodgings in episode 1, Lily on the stairs is humming "Somewhere over the rainbow", which was written for The Wizard of Oz in 1939. She also happens to wear bright red shoes, which feels like yet another Wizard of Oz reference. Interesting enough, the subtitles say that she is humming a different song, "Night and day" which she openly sings throughout the series and was already a hit in 1932. (00:44:10)
Character mistake: The firefighters state that the acronym for CPR is ABC for Airway, Breathing, Circulation. This is very outdated as in 2010 the American Heart Association changed the recommendation to CAB for Compressions, Airway, Breathing following evidence that compressions first in CPR saves more lives.
Character mistake: When the bodyguards enter elevators, they always enter last; they should be entering first to ensure it is secure. This is particularly visible in the hotel where the elevator can stop on any floor and Special Protection Branch does not have complete control of it as an express.
Revealing mistake: When Harrow and Nicholls are in what is supposed to be Queensland Police Headquarters, a window is visible with logos for Radio National and Triple J behind them. This shows that the scene was recorded at the offices of the Australian Broadcasting Corporation. (00:31:04)
Character mistake: Dan makes a reference to the movie "Planes, Trains, and Automobiles" (the movie he's planning on the family to watch). He starts a sentence saying "by the time John Candy says 'those aren't pillows'." John Candy did not say that line in the movie - Steve Martin did.