Chapter Two: The Weirdo on Maple Street - S1-E2
Factual error: When Chief Hopper and his fellow patrolman are standing over the lake, Hopper has a radio on his belt. The radio is a modern Motorola walkie talkie and at least a decade newer than it should be.
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)
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.
Revealing mistake: Mr Knight shoots Suzie Boreton - after the muzzle flashes and sounds stop the bolt of his MK14 EBR continues to move back and forth as if it's still firing. (00:30:30)
Revealing mistake: As Sgt. Cain and Chief Lain stand by Marjorie's dead body lying on the hotel bed, discussing her death from an overdose, you can see her stomach rise and fall slightly, though she's supposed to be dead. (00:18:00 - 00:20:00)
Episode #1.1 - S1-E1
Continuity mistake: The characters are looking at the Ten Little Soldiers. When one of them (playing the role of Blore) is banging on the glass, you can see the hands of the mystery writer ("Lombard") leaning against the base. He's leaning on the top of the display case in the next shot. (00:22:10)
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.