At the opening, Artemus and Jim are standing at the hitching post in a deserted town, where Artemus finds a flyer that warned the citizens to leave town before the sun is "at its summit" on June 5. Artemus comments that it's the fifth, and looks upward at the sun, saying, "And guess where that sun is," prompting Jim to look upwards at the sun too. Then they walk away from the hitching post, and the sunlight is coming almost directly in front of them, casting long shadows as it only would at sunrise or sunset.
At the end of the episode, Cadwaller writes E = MC^2 on the chalkboard, an equation having nothing at all to do with the geology of earthquakes.
When West and Gordon are in the mine they are trying to tip the car off the rails. There feet are not tied up, so they just needed to stand up and jump out.
Both Cadwallader and Artie refer to the State of Wyoming. This Territory was not admitted to the Union until 1890, approximately 20 years after the time of the show.
In a scene near the beginning West refers to the cavalry as the "calvary."