Agent Franke recites a newspaper article about the man guarding Lincoln's box at his assassination letting his guard down and admitting Booth inside.
In fact, the guard was not at his post and Booth simply walked in.
The aircraft shown as "Air Force One" is incorrect. It lacks the Presidential seal affixed to the forward fuselage.
During what's supposed to be a rainstorm, Air Force One is seen taxiing after landing. It's sunny with shadows on the ground and members of the ground crew are seen with no rain gear on despite the studio film effects of "rain" falling.
Sweeping a golden wings wall decoration with an electronic detector, the cops decide that it is radio-active. Instead of backing away and calling a special unit, they then proceed to unhook the decorative piece with their bare hands and carry it away.