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: 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 Rain shoots the Xenomorphs in zero gravity, their blood forms long ribbons and other splatter-type patterns. In reality, due to surface tension, liquid in zero gravity forms into spheres. The blood would not have remained 'stretched out' like it does.
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.