Continuity mistake: During the high counsel meeting, the front shot of Leslie Jordon, he puts on his glasses. It quickly goes to a shot of behind him...and we see him putting on his glasses again.
Plot hole: It's been established that if you die on the property, you remain as a ghost for all of eternity. However, in Season 8, Moira's bones are retrieved and buried in a cemetery so that her ghost can escape and join her mother. However not all the ghost's bones are buried on the property, we know for sure that the Black Dahlia was not buried on the property and it's not likely Tate, Vivian, Ben or some of the others are buried on the property as well so they should not be tied to the house.
Suggested correction: Tate's victims from the school shooting are ghosts who can move between different locations. There's nothing to suggest that the ghost of the Black Dahlia isn't merely choosing to be in the Murder House rather than being tied to it. The same goes for Vivien and Ben, since Violet is going to stay in the house, so might they.
Piggy Piggy - S1-E6
Continuity mistake: The people that Tate murders at school have different wound patterns. Episode 5 they say what Tate did to them, episode 6 shows the attack. Episode 5 the goth girl says Tate asked her if she believed in God before shooting her - episode 6 he asked her nothing, instead just shot her. Episode 5, the guy in the letterman jacket illustrates his wound to be a single round to the head - episode 6 he shoots the letterman with a shotgun in the chest, not a handgun to the head. Episode 5 the cheerleader shows no apparent wounds of being shot - episode 6 Tate shoots her in the face with a shotgun.
Afterbirth - S1-E12
Continuity mistake: When Stacy and Miguel (the new owners of the house), are making out in the kitchen, her shirt goes from off her shoulders to back on her shoulders across several shots.
Afterbirth - S1-E12
Continuity mistake: When Vivien and the maid are sitting in the kitchen, one shot shows the maid from the side with her hands in front of her on the table. The shot changes and instantly her hands are holding a coffee mug in front of her lips.
Character mistake: The doctor states that the devil resides in the "frontal gyrus, the occipital lobes" and taps on the guy's forehead. The occipital lobe is at the back of the brain. (00:35:50)
I Am Anne Frank: Part 1 - S2-E4
Visible crew/equipment: In the scene where Lana Winters imagines receiving an award for her expose while in line for her medication, her mic pack is visible as she steps up to accept it. It is not visible in the high angle long shot before she gives her speech. (00:17:15)
Character mistake: When Lana and Kit are speaking in the cafe, the window behind them contains a spelling mistake. The window reads "Bolyston Cafe" when it should say "Boylston Cafe." (00:31:45)
Bitchcraft - S3-E1
Continuity mistake: The voodoo woman stabs herself in the hand, inflicting a mark and drawing blood on the woman across from her on her right hand. In the very next scene, after the voodoo woman gets up and leaves, the woman's damaged hand has no marks. (00:23:40)
Visible crew/equipment: As the camera pans behind Kyle, the camera can be seen above his head in the mirror. (00:15:30)
Character mistake: At the table when Laveau admits she was the one who hired Hank as a witch hunter, Fiona tells Cordelia "You're not just blind, you're wilfully blind" and backhands her on the right side of her face, knocking her to the floor. On the floor, Cordelia is holding the left side of her face.
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.
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.
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.
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.
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)
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.
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)
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.
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.
