When the store clerk puts ice into the glass and hands it to Faith Hill/
Margaret Dutton, the ice gets progressively larger as the scene progresses.
Shea dismounts and sits down next to Elsa to tell her the story of the Apache scout. Once finished he rises and walks away without retrieving his mount. Next scene shows Elsa walking back to camp and retrieving her mount. A cowboy would not leave his horse unattended or at least hobbled.
One of the characters buys a small handheld mirror for $50. In 1883, that was a lot of money. In fact $50 in 1883 corresponds to about $1380 in 2022. The same goes for when sending the chef to buy groceries, he claims $600 to cover the rest of the journey. In 2022, that equals to about $16,500. That is a lot of cash just to pull out of your hat and hand over to someone that should visit the local grocery store.
The shotgun being held by Noemi has a polished wooden stock and a plastic butt plate. One could argue that such a refined weapon with polished stocks is possible in 1883 frontier, but not the plastic butt plate.
The fruit jar used to hold whiskey at the trading post is a 1920s Ball Perfect Mason. The beaded seal wasn't in use until 1900 or so. It should probably be a shoulder seal jar with "Mason's Patent Nov 30th 1858" embossed on the side to be authentic to the times.
The episode opens with Elsa in the wagon crying, while the wagon is moving. When she comes out of the wagon, she goes to Ennis' grave. He would have been buried where he was killed, not where they traveled to.