Continuity mistake: Inspector Bucket looks at the wallet Compeyson has placed on bar. The letter M has a few studs missing at top left. Later, when Bucket shows the wallet to Fagin, the M is complete. (00:18:25 - 00:21:50)
Continuity mistake: When the "Mole Women" are being interviewed on the "Today Show", watch the white circular table in front of them and the couch they are sitting on. The host has a small smattering of papers and a pair of glasses sitting besides him at the beginning of the scene. Throughout the scene, he will sometimes be holding the glasses and using them to gesture, sometimes not. And the papers move about from the couch, to the table, to another position on the table, etc. True, there are several shots where they are not visible, but it would make no logical sense for him to repeatedly pick up and move them between every shot where they're visible for no reason, and he is sitting in the exact same position in every shot, with his body language showing no movement towards them. They obviously shot the scene a few different times and he placed them down in different positions each time, and the scene was constructed with these different shots.
Factual error: As Ren enters Renautas and meets Emily, the word "Welcome" keeps scrolling in various languages on the screens in the background. Although hardly seen, the Hebrew is wrong, as it is reversed (text from left-to-right, as opposed to right-to-left).
Episode #1.1 - S1-E1
Factual error: The series is set in 1933, as the initial captions show. Yet the locomotive pulling the Orient Express is a JNR Class C58: the C58 series was built starting from 1938 (C58 239 used here is from 1940).
Continuity mistake: When Carolyn and Ennis are racing on the beach, Carolyn in side-saddle has both her legs on the left and for just a couple of split seconds in another shot they're both on the right, and then back on the left again after that.