The front license plate falls off when they are run off the road by the military vehicle. Later scenes show the license plate back on.
Windshield is shot during the standoff at winter wonderland. Remainder of the movie it is intact.
Although set sometime in the future, Jesse (Cailee Spaeny) takes photos with a manual wind film SLR camera. Seemingly having an inexhaustible supply of film canisters, which traditionally only have either 24 or sometimes 36 frames on the roll, she snaps away with abandon, never once stopping to reload or run out of film.
When Lee is lying on the floor in the White House, some of the shell casings next to her are 7.62mm blank casings. Identified by an elongated brass case in place of where the projectile would be.
While being pinned down under sniper fire, you hear the sound of the snipers gun before the bullets arrive to camera / characters.
A military helicopter will not turn on its navigation lights during combat.
The Apache helicopter is equipped with a 30mm chain gun, yet the tracers and sound is indicative of a Gatling-style minigun.
Early in their trip, they drive across the median of the highway, leaving deep tracks across the grass. Although it is clearly the only way to get through, before they drive across there are no tracks or ruts at all.
When the journalists are getting gas, their SUV is parked on the wrong side of the gas station. When Jessie gets out of the car you can see where the gas is filled and they parked incorrectly.
The sprinklers in the safe town have the tock-tock-tock sound of impact sprinklers, even though they are continuous flow sprinklers.