Factual error: In the diner, the kids listen to/dance to Britney Spears' "Toxic," which didn't release as a single until January 2004. This takes place in 2003.
Factual error: After the naval battle, Thraex is waiting for an informant who tips him off about Lucilla and Marcus Acacius's plans. And of course, as a well-educated gentleman of 200 AD, he kills time by reading the newspaper. Wait, what? Needless to say (to anyone but Ridley Scott, probably), ancient Romans wouldn't/couldn't exactly get their news by newspaper, the press having not been invented yet. This one looks so modern in its layout it even has headlines and a proper publication title, "Roma Viridia."
Factual error: The movie, by various accounts, takes place 300 years after the apes took over and humans were rendered "dumb" (both literally and in the (non-PC), mute meaning of the word) or went underground. But yet they're making contact with a communication satellite. Satellites don't function for 300 years; they require occasional course corrections to keep from entering the atmosphere and burning up. Course corrections require propellant. The propellant wouldn't last 300 years. And the electronics.
Factual error: When Raban meets the Baron Harkonnen in Harkonnen's bath, the water reaches nearly the top of the bath. As Harkonnen's large body descends into the liquid, the level of the liquid does not rise, in contradiction to Archimedes' principle. (00:46:37)
Factual error: During the scene inside the submarine, you see a Commander (O5) giving orders to a captain (O6). This would never be a thing on any vessel. You would have a Commander as a Commanding Officer on a submarine, but not having a Captain working for the Commander.