Character mistake: When John Henry Irons is arrested, two police officers lay him face-down in order to zip-tie his wrists behind his back. A close-up of Irons' hands, however, reveals that the zip-tie only wraps around his right wrist while crossing about mid-way on his left thumb, meaning that he could easily remove his left hand from the restraint with very little effort. Arresting police officers would never make this mistake in real life.
Character mistake: White says Exley's father died in the line of duty. Exley said he was off duty when he was shot, and he didn't correct him.
Character mistake: When Gilmore radios for backup during the Monument Valley chase, he is told additional officers will join them in Blanding. Kowalski hears this on his scanner as they pass a sign saying Blanding is 14 miles away. Kowalski then stops dead in the road and turns around, and the troopers do the same, yet when Sgt. Preston grabs the shotgun, he justifies firing on Kowalski saying "We're coming on to Blanding!" In actual fact they would be heading away from Blanding.
Character mistake: When Darcy walks into the police station the chief calls her Joan, the lead actress' real name, by mistake.
Character mistake: At the end of the movie, the rescue plane changes its callsign to Air Force One because the protocol is "Air Force One" is the callsign for any U.S. military plane (or, more specifically, an Air Force Plane) with the President on board, not just the blue and white 747. Thus, it would not be used for a plane on which the president is not on board. This is an important detail considering that for most of the middle section of the film, the terrorists believe the president has escaped and that they are dealing with a random secret service agent resisting them. The vice president and other administration officials dealing with the terrorists don't want them to know the president is still on board, as it could motivate the terrorists to threaten his family further. So, when the fuel tanker shows up to refuel the plane and addresses it as "Air Force One" to give instructions on the procedure, they are inadvertently confirming that the president is on board. To maintain the ruse, they should use the callsign "SAM-28000" or "Air Force 28000" when talking to the terrorists, referring to the plane's tail number. Similarly, any time an official makes a statement about the incident in public, they could refer to the plane as "28000" to keep up the ruse to the press (though it's not uncommon to refer to the 747s as "Air Force One" for the sake of simplicity in casual or non-official capacities, an instance of one plane communicating with another would not be).
Character mistake: When Jernigan chases the car, he tells the team, "It's heading south on Adams." The toy car then turns left, which means that the car should be heading east. However, Jernigan tells the team that the car is headed west.
Character mistake: When Alison is stalling Tanley from entering the bedroom where Haru is escaping being discovered, Tanley refers to Alison as "Angela darling." (00:41:33)
Suggested correction: He says "Oh, aren't you a darling."
Character mistake: When Barr denies giving Jeff's wife a ride, Jeff says this was in the last half hour or so - but considering the time it would take the truck to go to Belle's (5 miles away), the wife to call a tow truck, back from Belle's, then Jeff waiting extra time, then fixing the jeep, heading to Belle's, the time he spent inside, then driving along the road until he saw the truck would in no way be only a half hour...more like an hour or two at best.
Suggested correction: Jeff is obviously in distress because he can't find his wife. Is it not possible that because of the stress he's under, the amount of time that has passed is different for him? Besides, we know the wife never made it to Belle's. Later, we see she's been transferred to another vehicle.
Character mistake: When they first receive the alien signal, they decode it and play it as a TV signal which shows Hitler speaking at the opening of the 1936 Summer Olympics in Berlin. Kent translates what Hitler is saying as "I declare the Games in Berlin, at the celebration of the first Olympics of the New Era, as opened." Hitler actually says "the *eleventh* Olympics of the New Era." The "New Era" doesn't refer to some Nazi concept, it's used to separate the modern Olympics from the ancient ones in Greece.
Character mistake: Bentley mistakenly calls Melissa, the kidnapped sister of Ozzie "Gabby", which is the name of her friend.