Character mistake: Almanzo says he hasn't seen his brother Royal in 10 years, but in fact he saw him not long ago as he looked after his 2 sons who were terrors, and at that time Royal didn't even have a daughter.
Other mistake: At the very end, Mr. Hanson is seen walking toward the church. Because of his stroke, he's slow and unsteady. We see several close-ups of his feet, showing how he's struggling. Two of those shots are the same footage. It's obvious, because you see that he drags his foot over a small stick in the road and stumbles - and in both shots, it is exactly the same.
Continuity mistake: Charles is delayed getting home on his wedding anniversary because a wheel on his wagon broke, he had no jack and he had to make repairs during a heavy rainstorm. Rain is still falling late at night and can be seen through the window when Caroline hears Charles arriving. She runs outside to greet him and suddenly there is no rain.
Continuity mistake: At the end, when Lars Hanson hears the church bell ringing, he gets up from his bed and goes to look out the window. When he first gets up, his hair is completely tousled - definite "bed head." The shot changes to show him leaning out the window, and his hair is neatly combed. When the shot returns to the inside of the room, his hair is once again rumpled and untidy.
Revealing mistake: When Charles Ingalls plays his fiddle at the end of the episode, one can see from the movement of his hands that he is not really playing, but just pretending. (Also visible in every other episode where Charles plays the fiddle, but most obvious in this one.).
Deliberate mistake: When Mary gets to the school where she is going to be teaching, all the children are standing outside wearing shoes. However when they come in to the school they are barefoot. I have a feeling this was done to show how poor the community she was teaching in was supposed to be, but it looked like too cold and rainy of a day to let the actors be outside barefoot.
Continuity mistake: When Laura pushes Mrs. Pierce, she lands in a pail of water on her buttocks, and her hair remains dry. The next shot is of Laura saying something, then in the very next shot we see Mrs. Pierce still sitting in the bucket, only now her hair is soaked. Since she landed on her behind, her hair should not have been soaked, and there was no time for anyone to pour water on her head between the shots.