The Raccoon - S1-E10
Character mistake: Charles takes a bowl of water to Jack. Jack steps away from the water, and doesn't drink. Then a couple of scenes later, when Caroline and Charles are in the barn, Mary comes out and says Laura is thirsty. Caroline starts crying and says that Dr. Baker says that it's a sign, but a sign of rabies is actually when the person or animal doesn't want water. At one point, it was called hydrophobia because of the fear of water. (00:38:26)
Christmas At Plum Creek - S1-E14
Character mistake: When Charles explains to Carrie about Christmas, he mentions 3 kings and 3 wise men. The bible refers to them as Magi or Wise Men and no clear evidence on whether there were just 3, or if they were even kings. Putting aside the number of visitors and what they were called, it's either kings or wise men, but not both.