During the operation to save Bethany's life, Phlox removes a bullet from her right side. Later, when she comments to Archer that she feels fine and doesn't even have a scar, she indicates where she was shot by touching her left side.
The owner of the stable offers Trip a horse and saddle for $20. That would be an extreme bargain as a horse in the 1870-1885 era would have been between $100-300.
Archer tells the saloonkeeper that he would like to wait inside until it cools off, yet he is wearing a full-length coat, multiple shirts, and a thick hat - none of which he ever takes off.
However, it has been shown that long, loose clothing (such as Bedouin would wear), even from thick material, allows cooling air currents. Moreover, multiple layers of clothing would help to absorb sweat. European explorers often wore full suits of clothing, no matter what the heat.
During the shootout with Bennings' men, Archer gets shot in the shoulder from behind. The shoulder explodes forward quite clearly, but when Archer falls forward the back of the same shoulder is visible and there is no bullet entry. They squibbed the front of his shoulder but the back is perfectly untouched.
When the stable hand brings a horse out of the stall, for Trip and T'Pol to consider, it is already saddled and bridled.
The rifle Sheriff MacReady is carrying right after Archer's jail break is clearly a prop, and not a very well made one. The magazine tube is at least a few inches longer than the barrel. On lever action rifles the magazine tube is always shorter than the barrel, never longer.
Much of the equipment, furniture and technology used in the human settlements such as pistols would be impossible for a population of only 6,000. Even if correct for the time period of the abduction, such items depended on the manufacturing capabilities of much larger and widespread industrial bases.
None of the people wearing gun belts are carrying extra ammunition in their belt loops, the loops are completely empty on everyone.
T'Pol, had a problem with smells of people and especially Porthos, Archer's dog. And yet she walked into a stable with reacting or saying a thing. Surprising, since stable where horses are boarded will have a odor of horse manure. Vulcan's are supposed to have a very sensitive sense of smell.
And since this is a society living the 19th century life style. The stable wouldn't be the only place with an odor. Personal sanitation would be poor to say the least. And there would be many out-houses scattered all around. All of this would be added to all horses used for transportation, and animals kept for slaughter.
And not a word or wrinkled nose from T'Pol.