Several references are made during season 2 in regards to the Oklahoma "Indian Territories," where part of the action takes place. Oklahoma did in fact become a state in 1907.
Some of the cars in the freight train consist are not from the period era; especially those with steel construction and large "Santa Fe" logo, these belong to the 1950s.
In Spencer's encounter with the Ft Worth policeman (or whatever he was supposed to be), he was threatened with a vagrancy arrest. He should have still had money from his fight winnings, and he had valuables (a rifle) which could have been pawned or sold.