In one scene when President Moss first meets President Kirkland he is leaning on the desk, yet in the next scene, his hands are now folded in front of his chest.
The clock in Seth's office showing times in different locations is incorrect. Washington shows 14:13, so Kabul should show 22:43.
When the American hostages are pictured in Africa, there is a great deal of snow on the ground. The only places it snows in Africa are Morocco in northern Africa, South Africa and Lesotho in southern Africa, and high in the mountains. Even if snow were possible wherever the hostages are being held, it was earlier revealed that the country borders Zimbabwe, which is in the Southern Hemisphere. This is taking place in February or March, so it is the middle of summer in the Southern Hemisphere. It doesn't snow in Africa south of the equator in summer.
The car that crashes is shown having been "hacked" to where the steering and brakes are ineffective. That older model Lincoln had no such automated controls. Adding steering controls would have been noticed by the driver as the steering components would intrude into the driver's area. While some modern vehicles have automatic braking, they do not prevent the brakes from being applied. Without these controls, the car could not be remotely controlled, so it could not have crashed as shown.