The Lord is My Shepherd - S1-E13
Continuity mistake: In this episode, in the various scenes showing the church, the bell is gone but in the next episodes it has reappeared again.
The Raccoon - S1-E10
Plot hole: The plot gets confusing here. First, Laura and Jack (the dog) are rabidly bitten by Jasper (her pet racoon). The doctor warns they may have rabies from the bite. A second more dangerous raccoon is discovered which eventually left the area. In the end, Charles (discovering there were two raccoons in the barn after finding Jasper remaining), says Laura is going to be OK after all. The main confusion is that Laura would still be in danger from the bite regardless of which untested raccoon bit her.
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)
The Raccoon - S1-E10
Factual error: Laura and Caroline are playing a word association game about beverages and Laura says "orange juice, " which wasn't used by Americans until the 1920s. Any earlier than that, oranges were a luxury not available to farmers in Minnesota.
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.
Revealing mistake: The guys get the pregnant girl and her kids 50 lbs pounds of flour. She goes outside, people are talking about her and she runs. You can see tire tracks in the dirt road.
Other mistake: Charles can barely get up from his bed because of broken ribs, and it's totally impossible to breathe well, let alone moving sacks of grain. But in the end when the neighbors help with the sacks he's walking OK, as if he hadn't just fallen down from the top of the pile of sacks with broken ribs.
