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.
Revealing mistake: When Elly is "skating" on the black oil while fighting the bad guys, we can see that it is Bryce Dallas Howard's stunt double in a few shots where it briefly shows her face.
Factual error: In Episode 1 we see a view of the Vegas strip labelled 1956. We see several more recent cars including a 1963 Cadillac Fleetwood.
Factual error: Secret Service Agent Miles salutes the President inside of Air Force One and has the other hand on her hip. Secret Service agents do not salute. They are not military.
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.
Factual error: The movie is set in the US, but there are several things that give away the fact that it was shot in the UK. In one scene, a Tesco superstore can be seen in the background and the lift bridge seen in the film is Kings Ferry Bridge which connects the Isle of Sheppey to the Kent mainland.