Factual error: Adam Kendall goes to Minneapolis to take the entrance exam to law school. He meets a fellow student who, after the first exam, accompanies him to the "EL (the elevated train) " Minneapolis never had an elevated train, only Chicago.
Come, Let Us Reason Together - S7-E13
Continuity mistake: By this episode, the restaurant windows have been displayed as Caroline's restaurant (replacing Nellie's). Although most scenes here correctly display Caroline's, one scene that starts from the outside with the horses riding by, the windows still display Nellie's (happens about 3 times this episode - the last time is shown just before Nellie and Percival are laughing on the bed).
The Nephews - S7-E14
Factual error: Royal Wilder promises to give his sons an Indian Head nickel if they are well behaved at Almanzo's/Laura's house. The Indian Head nickel was not minted until 1913 - 30 to 40 years later.