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.
Factual error: Laura Ingalls Wilder was born in 1867. Ralph Waldo Emerson died in 1882, which means she was at the maximum 15-16 years old (and already married) in order to meet him IF he were to appear in 1882 which is not possible because: The problems with his memory had become embarrassing to Emerson, and he ceased his public appearances by 1879 (according to wikipedia).
Factual error: When the hot air balloon comes down with Carrie in it you can see N410AA printed on it. This is commonly called a tail number on planes and is issued through the FAA, which of course did not exist during the time period of the episode.
Factual error: This episode was mentioned by Laura at the beginning as taking place in December 1889. Rose was born in December 1886, so she should be 3 years old now, but she is shown through the episode appearing only to be roughly 6 to 12 months old and still in a crib.
Continuity mistake: The restaurant has "Caroline's" painted on the windows (except while operating as Mrs. Sullivan's). However, near the start of the episode, when the horses trot by in a nighttime exterior shot of the restaurant, the window still reads "Nellie's" (taken from earlier in the series). This same mistake has been seen in at least one other episode of season 8 as well.
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.