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.
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.
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.