Revealing mistake: When Elsa is waiting in the lobby, she's wearing a dress which shows her normal, not wooden legs. It's very apparent when she is crying on the floor.
Edward Mordrake: Part 1 - S4-E3
Factual error: Season 4 takes place in 1952. Elsa sings Lana Del Rey's Gods and Monsters. The lyrics say "living like Jim Morrison." Jim Morrison was not famous until 1960. He was born in 1943, which would have made him only 9 at this time.
Continuity mistake: When Paul spits on the left side of Dandy's face you see Dandy get up and wipe the right side of his face. Also it appears the blood in his nose magically disappears between shots. (00:03:15)
Edward Mordrake: Part 1 - S4-E3
Deliberate mistake: After Elsa kicks Bette and Dot off the stage, Elsa looks at the sheet of music on the stand and you see the name of the song 'Criminal' and it also states it's by Fiona Apple which is true, but this season is set in 1952, and Criminal wasn't released until 1996.
Deliberate mistake: Conjoined twins Bette and Dot have freckles and moles on their faces and necks in the exact same places.
Suggested correction: Not technically a mistake; unlike regular twins, conjoined twins are always identical in appearance, contrary to what movies/TV suggest. This could easily include mole patterns.
I looked up "conjoined twins" on Google images, and there are numerous photos of conjoined twins having freckles and moles in different spots. Notably on the Hensel twins, Brittany has a mole on her chin, but Abby does not. This disproves your suggestion that conjoined twins are always identical in appearance and could have identical mole patterns.
Continuity mistake: When Elsa reveals her prosthetic legs to Dot and Bette, they are two inches below her kneecaps, when in prior episodes they were just beneath.
Blood Bath - S4-E8
Revealing mistake: Elsa's legs are supposed to be wooden prosthetics, but when she walks away from Ethel, who's holding a gun at her, it cuts to a shot of Jessica's calves which bend slightly as she walks. (00:00:14)
Revealing mistake: When Dandy shoots Penny through the sheet, the second sheet flies out as it's hit with blood. But the sheet he shot through has no hole in it.
Edward Mordrake: Part 1 - S4-E3
Factual error: During the Bette and Dot surgery dream, we see the bone saw machine brought in and it says "Easymatic 300." In actuality, the machine is the power source for an X-Ray machine and wasn't produced until the early 1980s, while the season takes place in the early 1950s.
Other mistake: When Dandy goes on his shooting spree, the pistol he uses holds 9 rounds. When Jimmy returns to find everyone dead inside the main tent, there are 11 dead bodies laid out.
