At the start of Act I, the scene is identified by a title as 'State Capitol' - with an 'o'. That spelling is used to identify the actual building where the state legislature hold office. The city where the government is housed is the Capital - with an 'a'.
During the opening, a caption identifies the location as the "Southwest Territories". There was never such a designation for any part of the United States. As originally constituted on 9 September 1850, the territory in which the actions of this episode take place was comprised of what is now the states of New Mexico and Arizona, parts of what is now southernmost Colorado and Nevada; in 1853, the area of the Gadsden purchase was added. Originally divided by an east-west boundary with New Mexico in the north and Arizona in the south, it was later divided along a north-south line that remains as the current state boundary.
Near the end, when West follows a man to the blacksmith's building, the man unlocks the door with a key, and enters. The face of the lock panel on the door is flat and smooth, with a simple keyhole in the lockset. In the close-up of West picking the lock, the face of the lock panel appears rough, with a pattern of vertical stripes, and a raised bezel around the keyhole. After that, all other scenes show a smooth lock face again.
The railroad passing through Pinewood is designated the "Tucumcari-Tucson Railroad". The settlement was not founded until 1901, as a construction camp for the Chicago Rock Island and Pacific Railroad. Local violence earned it the name Six Shooter Siding. In 1908, the now permanent settlement renamed itself after the nearby Tucumcari Mountain.
At the opening, West and Harper split up, with Harper heading for the "state capitol". They're operating in Arizona, which was the last of the 48 contiguous states to be admitted (14 February 1912). At the time of these events, it was Arizona Territory (proclaimed 24 February 1863), with a territorial capital (see also Trivia).
The episode takes place during President Grant's term, somewhere between 1869 to 1877. However, the Kinetoscope wasn't invented until the late 1880s and wasn't widely used by the public until the 1890s.
They show in detail how the innocent subjects are "conditioned" to carry out the violent instructions of Raven. However they never show how they receive these specific Instructions and each is very different.