Factual error: In the first part of the story-telling the main character appears to be in front of a wrist-watch store's window. That store is Richard Mille, a brand that only started making watches in 1999, the story is set in 1987. (00:06:05)
Visible crew/equipment: When Dani hands the spider back to Miles after he uses it to scare Flora, just after she says "Including me" and the spider moves from Dani's hand to Miles' hand, a red tape marker can be seen on the ground right under Victoria Pedretti's left foot. (00:34:09)
Factual error: The British schoolroom has a UK flag at the front. American schools might do that; UK schools don't. There's even a little one on the teacher's desk.
The Two Faces, Part One - S1-E3
Factual error: The British policeman carries an American-style long baton on his belt. No British police force used batons before 1994 (the series is set in 1987), and batons of this pattern were never used in any case.
Factual error: Dominic Wingrave says "it took me 6 years to do the math." Not something any British person would say - in the UK it's always "maths."
The Two Faces, Part Two - S1-E7
Continuity mistake: The first time Peter is inside the memory with his mother, two ornamental flags can be seen hanging on a wall next to a light switch as they talk in the living room. One of these flags suddenly turns roughly 45° to the left without anyone touching it. (00:07:33)