When in the courthouse, Jerimiah has the horses of the town stampede and wreck the boardwalk outside of the courthouse. Jim and Arty, and others, go outside to inspect the damage. While outside, the abundance of light (obviously filmed during daylight hours) shows nowhere else was damaged by the stampede. BUT when everyone goes back into the courthouse, the camera shot from inside through the open doorway shows the absolute darkness of the night. So, from outside it is quite light, and with the next camera shot from inside, it is pitch black.
When Carl Jackson unlocks the smokehouse at the very beginning of Act 2, it is apparent when he turns the key that the deadbolt was never engaged - it would have been visible through the gap between the lockset and the strike plate.
Early in act two, they have a fife that needs to be played and ask Artemus Gordon if he can play it. He says he can. The next scene he's "playing" the fife by sticking the whole end in his mouth. Except that you don't put a fife In your mouth to play it. You only set it to your lips and blow down into a small hole which is a few inches from the end. Clearly he doesn't even know how a fife is played.
Jim and Arty concoct a devise to fire pepper at the bad guys. It goes off and the bad guys are overwhelmed by the pepper and sneeze uncontrollably. Jim and Arty rush their adversaries and beat them into submission. And though the pepper cloud overwhelms the bad guy, when Jim and Arty step into the area where the pepper cloud is (where it overwhelmed the bad guys), it has NO effect on Jim and Arty.
A couple of minutes after the opening credits, the sheriff read a portion of the letter summoning James West to the community: "Dear Mr. West- It is urgent that you come at once to Mills Creek." Throughout the rest of the episode every building sign in town called the community "Mill Creek."
In the opening scene inside the cave, Artemus Gordon has trouble holstering his gun. A trained and experienced Secret Service agent would have no problem returning a gun to its holster.
Jim and Arty shoot the "ghost" at close range, and exclaim surprise that they did not kill him. They discount the possibility that he might have been wearing a bullet proof vest. But silken "bullet proof vests" were developed at the end of the 19th Century, and The Wild Wild West takes place during the Grant Administration (1869-1877). So, the concept of a "bullet proof vest" was still 10-20 years in the future.
When the horses are stampeding a riders leg appears on one of the horses.
At the end of Act 2, when the camera zooms in on Carl Jackson, the camera shadow is visible on the curtains to the left.
In explaining the story to Elizabeth, West states that Jeremiah witnessed the murder years ago but could not report it because the war had just started. Earlier when he ghost of the murdered man is "channeled" by Jeremiah, it reveals the killing took place as rumors of a great war were in the air. Yet the visible "ghost" is already dressed as a Confederate colonel, implying he lived to serve.
When Jim is miniaturized, Antoinette had to make him new doll-size clothes but, when he was brought back to normal size, the doll-size clothes magically expanded to fit him.