Clem's dress at the end of the show, long after Lee has become an attorney, is a style from the 1890s. However, the first published version of the song "Frankie and Johnny" did not appear until 1904.
The men in the first scene have belt loops on their trousers. These were not invented until the 1920s.
In the saloon scene, a character casts a shadow on the exterior backdrop.