Breecher purposefully does not sign the hotel register so he can remain incognito, yet later Alice calls him by his last name (which he hasn't yet given to her or anybody in town).
Beecher tells Dandridge he's been sentenced to hang and then hands him a document. However, as shown on screen, the document is merely a warrant authorizing Beecher to apprehend Dandridge and bring him before a Justice of the Peace. Ditto for when he encounters Huxley.
Reginald said his wife was buried beneath a willow tree, but when Reginald's grave is shown next to hers, the long-shot shows the tree they're buried under is definitely NOT a willow tree. Even worse, the tree in the close-up is clearly not the same tree in the long-shot. The long-shot tree has four trunks and the close-up tree has only two trunks.
Those who had fought for the Confederacy lost voting rights, but very few were otherwise punished.
Alice was correct when she called the horse a him as the horse was decidedly a gelding, not a mare. Breecher was wrong about his own horse's gender.
The Chapter 2 title card reads The Cooke's. Since it was referring to a family (the plural form of at least two people) whose last name was Cooke, the title card should have read The Cookes, without the apostrophe, since an apostrophe indicates the possessive form.
The Sheriff is supposed to be controlling the town with an iron grip, yet he apparently has zero control over the telegraph operator (which is the easiest way to alert the outside world of his corruption). Alice has no apparent difficulty in communicating with Breecher's boss.
When Sarah pulls up a bucket of water from the well, the rope is held in place with two Phillips head screws. Those weren't invented yet.
Living in the late 1800s in the American West, Honey has shaved armpits.
Around 1:09 Mathias and barkeep exchange:
"Not a fan of the job?"
"Not a fan of the man."
Breecher tells Alice his brown mare is outside. She replies: "I'll see that he's properly tended to". A mare is a female horse. She would know that.
Quaid was standing in the clear a full two seconds before he shot Reginald, yet neither Sarah nor Breecher, who both had loaded guns, got a shot off until after the fatal bullets had already been delivered, making it at least 5 seconds that they failed to act as their "tough" characters should have in a gunfight.