When Joshua and Skye are carjacked, the carjacker says that they've got the only running car in the city. The carjacker drives away, Joshua and Skye are left walking down the street. Another car drives by clearly visible behind them.
The same actor (Patrick Ian Moore) plays the sniper who first fires at the giant robot, as well as the guard who is immediately vaporized as a result. This exact same sniper footage was used when the military shoots Skye at the end of the movie.
Newborn babies can not hold their heads up on their own. They are also not that large or that clean immediately after birth.
Upon reviewing the interrogation, he flips a switch to shut off camera replay. No CCTV cameras work this way.
Inside First Congregational Church, a woman prays with a rosary, and after Josh asked her about Father James, later steps forward and crosses herself, then goes back to kneel. The sign of the cross, the rosary, the priesthood, and kneeling are mostly Catholic and thus non-existent in Congregationalism, which has pastors and adheres to the priesthood of all believers.
At the end of a scene where no cars are supposed to work, a police car appears passing by in the distant background.
When the car carrying the pregnant woman is being tailed by a car only a few feet behind them, they hide in a garage and as the shutters are being lowered the trailing car passes by, duhh did they not see the car drive into the garage.
At 51 minutes, while being pursued by a car Joshua runs OVER the length of a parked car, from hood to roof to trunk, rather than run around it. While perhaps done for dramatic effect, this would actually slow his escape as well as risk injury.
A US soldier wearing a sun visor seems a strong unlikelihood.
The hero is tied to a table and the scene shifts to show the beginning of Earth's destruction. The camera goes back to the hero and somehow he has freed his hands and is getting off the table.
In the scene where Josh is relieved of his duties and he enters his car and leaves a camera and a crew member is visible. First in the driver side window when he fully opens the door. Then across the car when he pulls off.