Factual error: The film opens stating how a series of worldwide events destroyed major cities in the year 2019, and then the following scene shows a subtitle saying "three years later", implying the film's events take place in 2022. There are entire scenes where the President is rallying supporters for his re-election, however this is impossible since 2022 is not a presidential election year.
Continuity mistake: Gerard Butler seems to have the ability to grow a full beard in less than a day, when in some scenes he's only got a few days growth. One example is when he hits the deck of the station donning a full beard, and then he's almost clean shaven when going through a locker. (00:32:30 - 00:43:20)
Visible crew/equipment: Near the end when they kidnap the president and steal the electric car, you can see a stunt pad marked with a yellow "x" as the 2nd secret service agent jumps to the ground while avoiding the car coming out of the parking garage.
Continuity mistake: As Hannah walks away from her dad, she is replaced by another little girl for a second. (00:26:25)
Suggested correction: It's the lighting and shadow. It is Hannah though.
It is definitely not the same girl. They aren't even the same height or shape.