In the introduction, Dot speaks of the 3rd of September, and it being a Saturday. We then learn this is set in 1952. In 1952, Sept. 3rd was a Wednesday.
In the ending scene when it is revealed that Elsa has legs made of wood we can clearly see the actress' real legs when she removes the stockings before taking off the wooden legs.
There's a scene where Bette takes a drag of a cigarette, but then Dot exhales it. However, the doctor (in the beginning of the episode) explains that they have four lungs without any mention of them being connected, so it would have been impossible for one to breathe in the smoke and the other exhale it.