In the bar scene, when Murdoch is interrogating the barwoman, Scott Joplin's "Paragon Rag" plays in the background. This episode is meant to take place in 1899, but "Paragon Rag" was first published in 1909, ten years later.
The man stalking Anna Fulford uses the two-handed grip on his pistol. But this technique was unknown at the time. It was first developed by Jeff Cooper in the 1950s.
Brackenreid uses the expression "Cooperstown's Finest" as Crabtree throws a baseball in police headquarters. As a matter of fact, in 1899 there was a great controversy whether baseball was even invented in the U.S. at all as many thought it a variation on the British game of rounders. The fallacious claim that the game was invented by future Civil War hero Abner Doubleday in Cooperstown in 1839 stemmed from the findings of a 1909 commission formed by Albert Goodwill Spalding tasked with discovering the origin of the game. Its dubious conclusion was based on a letter it received by a septuagenarian with a penchant for tall tales and a weather-beaten hand-stitched baseball with no provenance. Doubleday never claimed to have invented baseball in Cooperstown or anywhere else. In fact, documentation exists that the game was being played in 18th Century Massachusetts. In order to boost tourism in their small New York State village, a baseball museum was dedicated in Cooperstown in 1936 and founded with its first five inductees in 1939. Brackenreid would have had no reason to connect Cooperstown and baseball ten years before Spalding's committee came to its dubious conclusion.