The Washington Monument is shown as almost complete. In 1876 the Monument was still only one third complete and construction had been stopped since 1858. Addition construction was authorized during the Centenial but actual construction did not resume until 1879.
In the shot at the large lake toward the beginning of the movie you can see what looks like a white buoy floating in the background. White plastic floating buoys did not exist in the time of the movie.
When discussing the super weapon with Burke, Turnbull claims Eli Whitney started the Industrial Revolution with the invention of the cotton gin. While that was an important invention of the era, the Industrial Revolution actually started in the United Kingdom.
During the final fight scene Jonah Hex fires a gun into a box of dynamite and lights a fuse on one of the sticks. For safety dynamite and fuses/blasting caps are keep separate until just before they are set.