The horse bucking happened by accident because the horse did not want to be ridden in the summer heat. The script just called for the horse to run away, but the bucking looked great and fit better with the story, so it was kept in the picture.
The hats hanging on the walls in the Hamilton home are there to cover the electrical light switches and thermostat that did not fit into the time period of the movie.
The quote that is framed on the wall of the Hamilton dining room ("Hope and Keep Busy") is by Louisa May Alcott, the writer of the novel on which the film is based.
The last shot of the film before the end credits was from after the director yelled "cut." It's not the actors acting as their characters, but rather them just being themselves, laughing and hugging.
The actor who plays Edith's father is her actual cousin in real life. He was chosen for the part because the role called for someone who resembled Edith, which he does.