Chapter One: The River's Edge - S1-E1
Revealing mistake: When Hermione opens the bag of money, one stack says "Motion Picture Use Only." (00:29:45)
Continuity mistake: When Riggs is hanging from the tree, his hands are tied behind his back. When he falls and lands on his back, his hands are still behind his back. In the next shot of him, his hands are now tied in front of his body, even though he didn't have time to do anything to get his hands there.
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.
Continuity mistake: When James is taking pictures from a car as men are entering a hotel, in the shots of him head on he is using a Canon EOS camera with a 70-200mm white lens. In shots from the side he is using a Nikon camera with an older Nikon lens. (00:27:35)
Plot hole: They only take out the shrapnel from the gut shot - they never deal with the shrapnel in his shoulder at all. (00:04:25 - 00:05:00)
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.
Other mistake: When Cobb starts to chase the red Dodge, there's a shot of him passing between two vehicles (and very distinct buildings in the background). When Murphy picks up the chase, this same shot is reused, showing her passing between the same two vehicles.
Other mistake: In this true crime show there are both reenactments and actual police photos used. The narrator states that thousands of rounds of ammunition were found in the home where a crime was committed. But the accompanying "Actual police evidence" photo that's supposed to be ammo is actually stacks of Kodak Slide Carousels. (My dad was a photographer and we had these in my house.) (00:29:15)
Visible crew/equipment: While Michael sits outside of a hospital room in the hallway, there is a clear reflection of equipment in front of him. (00:21:00)
Factual error: You can see the Unicredit Tower on the Milan skyline - the episode should be set in 1997 but the unicredit tower was built in 2012. (00:31:00)
Factual error: Almost all the people being shown skydiving have no experience doing it, but the instructor allows them to jump out of the plane unassisted after only giving a theoretic introduction into the subject. First time skydivers are always assisted in some fashion, usually through a tandem-jump or a parachute opened by a line attached to the plane.
Continuity mistake: Harry drives away from a crime scene and his rear numberplate is visible as D703 VAN. We then see Harry in his car from the front, and the numberplate has changed to E160 HLT. (00:21:18 - 00:22:31)
Continuity mistake: Christian is wearing a blue polo shirt, standing outside the luxury van in which Letty and Javier are being held captive. When he gets in the van, from that point on he is wearing a tan jacket over his shirt.
Continuity mistake: The father of a teen girl murdered in CA receives a letter from a self-proclaimed psychic concerning the murder. He received it at his home in RI, but the letter is addressed to San Diego, CA. The address is shown twice. (00:08:00 - 00:14:00)
Factual error: Cars in Thailand drive on the left side of the road with the steering wheel on the right, unlike the ones shown in the episode.