Factual error: When they show the capital building in Washington DC it is still under construction, but it was actually finished in 1864 - 5 years before the movie's set.
Factual error: West and Gordon are outfitted with massively powerful magnetic collars. Somehow the two collars don't interact with each other at all until they try to remove them, when they prove able to attract each other from at least 20 meters. Gordon rationalizes this by saying that they accidentally reversed one magnet's polarity, but if this were so then the magnets should have originally opposed each other with the same force, instantly throwing each other apart as soon as they were brought within meters of each other. Nonsensical.
Factual error: The amount of nitroglycerin in just one bottle at the beginning of the movie would be enough to level the whole brothel. Yet, when a cart loaded with bottles of nitro (or at least one full crate) goes downhill and explodes, it only makes a big fireball.
Factual error: Gordon shines a light through the back of the disembodied scientist's head to project his last visual image onto a screen. When the image on the screen is inverted Gordon remarks that "Refraction of the lenses causes the image to appear upside down". True; when an image passes through the lens at the front of the eyeball the lens inverts the image and it is upside-down when it hits the retina. However, Gordon is projecting the captured image on the retina back through the lens of the eyeball and onto the screen. When the image passes back out the lens would invert the upside-down image and return it to its proper orientation. The image should have been right-side up when it hit the screen.
Factual error: At the beginning of the movie, we see that the scientist who was killed was wearing his glasses. Hence, his last image would have been a clear one. Of course, the whole process of projecting a man's last sight by means of a light shone through his retinas is preposterous.
Factual error: As Jim and Artemus leave the White House heading for the Wanderer, they both head south. However, if they're taking a train from Washington to the west in 1869, they've got to use the B&O's track. The B&O station was north of the White House.
Factual error: The nitroglycerine would have exploded when McGrath's men threw it roughly onto the cart, leaving no risk of it exploding later when West makes his comment that this is not the way you transport nitro.
Factual error: In one scene Jim West is walking up to the White House. There is a cast-iron gate surrounding the White House, as there is today, but he gate was not added until the 1930's.