Episode #1.1 - S1-E1
Other mistake: When detective Campbell is making his speech to the officers, the board behind him has dates ranging from 1966 - 1975.
Chapter 13 - S1-E13
Other mistake: When Lucas and Zoe are at the restaurant, Zoe steals the staff list from the kitchens. It is an established fact that a waitress named Stephanie works in the restaurant, however when the camera closes on the list, her name is not listed among the other staff members. (00:32:40)
Other mistake: The URL seen on Siobhan's laptop (https://internet-search.comm7986/index.html) is obviously a fake URL.
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)
If I Should Fall from Grace with God - S5-E7
Other mistake: End of episode 6 it's nighttime in LA, they also show Bridget in a church in NY, where Terry is in confession. Beginning of episode 7 it's still nighttime in LA, when Terry walks out of confession it's daytime in New York. It does not make sense for Terry to go to confession mid episode 6 (during daytime in LA).
Other mistake: When Ray is interrogated by Hamer, he states that Clyde drives nothing but a V8 Ford, but in the scene immediately afterwards, Bonnie and Clyde show up at his brother's house, driving a 4-cylinder Model A.
Other mistake: When Spector is sitting up with the help of his nurse, the subtitles say [Spencer groans]; I think they mean "Spector", and he was the only man in that scene. It makes sense that he was grunting while sitting up.
Other mistake: The subtitles refer to the men cheering for the female soldier that was stripping as "Marines" despite all of them being in the Army. (00:24:10)
Other mistake: When Rebecca is telling Dorn about Etienne's death, she explains that his room was right above the garage and after the explosion she "tried to go in, but the room was gone." Yet at the end of the episode when Louis goes into Etienne's room, it is fully intact, including pictures taped to the wall.
Other mistake: Agents say they have seen seismic activity in South Dakota, but from earlier episodes, Daisy and Lincoln visit South Australia to find out Fire Guy.
The Daughter of Autolycus - S4-E5
Other mistake: Lady Felicia says "Ah, Father, how very propitious." The subtitles say "Ah, Father, how very capricious." (00:03:10)
Other mistake: When Greer and Castleroy are having dinner together he asks Leith to pour wine for them, but what comes from the jar is water. (00:15:45)