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.
Continuity mistake: As the tank pulls out of the lagoon, it has no seaweed on it until it is fully out of the water.
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.
Continuity mistake: After Gordon gets dragged across the sand by the magnetic collar, he lies 30 cm away from it, his right arm straight. Then West shows up, and angle back to Gordon, who's now just 10 cm away with his arm bent. If he had dragged himself upwards between shots sound had had to be heard.