Artemus Gordon enters the death chamber and points to the oversized switch used to activate the electric chair. When Gordon approaches the switch it is exactly perpendicular to the floor, but when the camera angle changes, it has suddenly dropped somewhat from that position, even though the shot changes too quickly for anyone to have touched it.
In the opening teaser, Jim West enters the Prince's hotel room, the camera switches to the face of the statue, the arrow is missing from the statue nose as if it has already been fired, the hole for it is clearly visible. When Jim West moves to just by the statue, the arrow is in place.
When the warden opens the safe the backside of the door and the frame are perfectly smooth. There is no latch and catch mechanism of any kind that could have locked it.
When Adams opens the closet door next to Jim's room, he doesn't insert the key far enough into the keyhole to do anything.
A prisoner is sentenced to be executed in the electric chair. The first use of the electric chair was in the 1890s. The first chair was built in 1889; the first man to be executed was William Kemmler in New York's Auburn Prison on 6 August 1890. The process took eight minutes and resulted in the body catching fire.
Gordon alludes to famous stage actress Lillian Russell. Russell would not achieve that breadth of notoriety until the 1880s. At the time of this story, she would have been about 12.
The Federal Bureau of Prisons was not established until 1930.