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 Four: The Moveable Feast - S1-E4
Audio problem: When Father Keane is speaking with Mother Bernadette outside, when Mother Bernadette says "The gift doesn't reside in you or me", and "Where you coerce and compel, we use compassion, forgiveness, and patience", her lips do not match what she is saying.
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)