At 3:14, both Timothy and his dad are wearing pants with belt loops, and the dad is wearing a wide leather belt. Before the 1920s, trousers did not have belt loops. In modern times, men started wearing belts in the 1920s, except for some military uniforms.
When Caroline puts on her red shawl and sits with Charles at the table, shiny nail polish can be seen on her fingernails. Nail polish first came to America in 1916. This show takes place in 1880 something.
Doctor Baker says he can't be certain but he believes Timothy has appendicitis and tells the boy's father to take him to Mankato because he can't do the surgery. However he had previously diagnosed Mrs. Oleson with appendicitis and had successfully operated on her. If he had successfully diagnosed and operated on someone before he should be able to do it now.
If Mrs Oleson already saw Reverend Danforth's spectacle in another town, she would have known he was a fraud, with the first service in Walnut Grove, when the same "sick" people came up to get healed, like in every town.
Grace is only shown for one brief moment. When the family is having dinner with Reverend Alden, she is not in her high chair as she usually is when the family is eating. She is also not with the family at church after the new reverend says he will be holding meetings on Sunday mornings. She is however, sitting on Laura's lap during the final church service.