Plot hole: Lori managed to get to the bunker through the elevator because the modern board was still replaced by the antique one. But that implies that she was able to call the elevator as normal. And if people can just call the elevator back but the normal control board has been replaced, then they wouldn't be able to use the elevator as normal, creating quite a problem in a huge hotel. Sydney earlier was not able to switch the board back to the normal one since she went out from a (mysterious?) exit/entrance, so this situation makes no sense.
Other mistake: The episode begins with a caption; "Chicago, 1930." In present day, through internet magic (hotel records from early 1900s somehow digitalized and publicly available!) Nigel and Sydney talk about the history (fictional, no actual historical basis) of the Roxbury. Nigel says that the original owner went out of business "after the war", then the company was sold, and the hotel refurbished, despite being, Sydney says, "only 5 years old." Later in the episode, Sydney looks at a plaque from the Chicago Historical Board that dates the elevator as "circa 1901." (00:12:35)
Continuity mistake: In the prologue, Young Murray finds a man he does not know sitting at a table. He advances towards him in a wide shot of the room, and the man positions his left hand on the corner of the table, but in the following closer angle on him, his hands are close together exactly like in the initial shot by the same angle. It's like the middle one never happened. (00:03:10)