Factual error: In several episodes, agents are handling biological material wearing blue nitrile gloves. The season takes place in 1983 but these gloves didn't come into use until the mid-90's.
Other mistake: The recap of Episode 4.1 has a scene that hasn't been shown until episode 4.2 or 4.3 where the FBI neighbor gets hold of Jennings in his garage to confront him on his alleged affair with his wife. The similar issue with another episode is seen in episode 3.12 or 3.13. (01:00:00)
Continuity mistake: Paige's wristwatch hands go forwards / backwards during the scene as she speaks on the phone with Elizabeth.
Continuity mistake: The Clock on the wall of the Jennings' home reads 1:25 am when Elizabeth calls her, but Paige's wristwatch shows a different time.
Continuity mistake: Elizabeth's hand on Gabriel's arm changes positions shot to shot.
Continuity mistake: Paige and Elizabeth walk into a parking lot, immediately passing the front of a sedan parked near the parking lot entrance. However, the scene changes to their front and the same sedan is parked further in, as the duo take a long time before passing the same car.
Continuity mistake: During the conversation between Elizabeth and Pastor Tim in his office, the Pastor's arms are instantly either raised or in his lap, occurring several times in the scene.