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)
Revealing mistake: When Bob and Joyce have lunch, Bob pops open a can of soda (which is period appropriate). The scene cuts to Joyce, then back to Bob. It is clear from how he is holding the can, and how he pretends to drink from it, that his newly opened soda is actually empty.
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: A typewriter is being used, but the carriage is not moving. (00:42:50)
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)