When Liston Day is in the cemetery, the grave he goes to has the name Caroline L. Day on the head stone. When West, Gordon, and the sheriff reach him, the headstone is gone.
It's established in the series premiere that president Grant is the president in the series, and that West and Gordon work for him. The story line states that Liston Day has been in solitary confinement for 30 years, and was sentenced on April 23, 1836. This would put the events of the story around 1866; three years before the Grant presidency began. The treason alluded to, however, occurred during Texas' revolt for independence, from the dictatorial rule of General Santa Anna, as led by Sam Houston. So, it would have been more accurate to state the interval of time as thirty-five years..
Day claims that his rats will be infected with bubonic plague by exposing them to plague carrying ants. Only fleas can infect rats or people since ants are not blood suckers. However, the discovery that fleas were the vectors of Yersinia pestis (the bacillus that causes bubonic plague) was not made till 1894. So, this was literary license to prevent anachronism.
Right after everyone enters the house, as the Sheriff enters the second room, he holds the lantern with his left hand out to his left. BUT the lantern casts the Sheriff's shadow behind him, at a 45-degree angle. This error becomes even more obvious when Jim takes the lantern, holding it out in front of himself. Yet the shadow the lantern casts this time is in front of Jim on the wall in front of Jim, even though the lantern is between Jim and the wall. Obviously, it is the set lighting behind Jim, on the other side of Jim, that is causing that shadow.
When Jim is telling Artie that he thought the prisoner's face had changed and he looked much younger he says that maybe it was the moonlight. Well there couldn't have been any moonlight because all of the shutters on the windows and the doors had been closed and locked shut because they were imprisoned in the house so there could not have been any moonlight coming in.
When the group enters the house and they move into the first room, as Artie and the prisoner move towards the chair, a spot light moves across the floor to light up the chair.
Day claims that the Black Death eradicated 3/4 of the population of 14th-century Europe. In fact it was much less, closer to 1/3.