Character mistake: Neelix says that the Great Wall of China, prior to the 22nd century, was the only man-made object visible to the naked eye from orbit. This statement has been long-since debunked, but it's not unreasonable to think the myth perpetuated itself in the future. Still wrong though.
Character mistake: Captain Janeway states the temporal differential ratio is .4744 seconds per minute (meaning for every minute on the surface, only .4744 seconds pass on Voyager). Tuvok calculates that 30 minutes on Voyager would be 2 days 11 hours and 47 seconds. However, at that ratio, 30 minutes would be 2 days 15 hours 14 minutes and 15.9 seconds. Later Tom (who was on the surface) says the last two months for them was only 2 days for B'Elanna (who was on Voyager). But with the temporal differential, 2 months on the surface would be less than 12 hours on Voyager. 2 days on Voyager would be almost 253 days (almost 8.5 months) on the surface.
Character mistake: Captain Janeway's main goal in this episode is to proceed to the holodeck and shut down the lightning shield protecting Chaotica's death ray so Lt. Paris can shoot it with his destructo beam. Throughout the scene where Lt. Paris further briefs Capt. Janeway on her way to the holodeck, the plot is such that her goal is to shut down the death ray, not the lightning shield.