Continuity

Frances Conroy ("Old" Moira O'Hara) is right-eye dominant. Many times you can see that she, as Moira, is focusing on the object she's looking at using her "blind" right eye instead of her left eye.

Anachronisms

Throughout season 4, ETC Source Four lighting fixtures can be spotted hung above the Freak Show stage. The Source Four wasn't manufactured until 1992, 40 years after the season is set.