(At around 14:02) Jackson pats Palmer in the arm with a dusted hand, leaving a lot of dust on Palmer's coat. 2 seconds later, no sign of dust on the coat.
Jonah mentions Calvin Oklahoma. Oklahoma didn't become a state until 1907. In the "Old West" it was Indian territory.
Mick repeatedly fires lever action rifles without cycling the actions. That is not possible, as once the chambered round was fired, the action would need to be cycled to reload and fire again.
When Mick and Turnbull are facing off in the saloon, Mick pulls out a Zippo lighter. Zippo's weren't invented until 1932.
The Searcher's gun is not loaded.
When Palmer, Jackson, and Heywood are confronted by Turnbull henchmen while they are looking for information on Turnbull Palmer states they are from the Internal Revenue Service. The IRS was called the Bureau of Internal Revenue from the time of its founding in 1862 until the 1950s when it was renamed.
When Jonah Hex asks about Rip, Sara states he is MIA. MIAA wasn't used to describe someone as Missing In Action until 1944. Jonah would not have known what she was talking about.
In the saloon, when Hex pulls his guns, the gun cocking sound is heard. It is then heard again as he levels them at Turnbull. In the response to this when everyone in the saloon pulls a gun, one of the gun cocking sounds heard is that of a semi-automatic pistol, which did not exist at the time.
Turnbull talks about the Colt Single Action Army (SAA) revolver being the gun that won the west. They were in 1874 when he said this. The SAA pistol was not introduced until 1873, so it was a brand new gun at the time and would have seen limited use by1874.