After the Presidents steal the station wagon from the campers, you see them zoom out on to the road taking a sharp right turn. If you look in the windshield it is apparent that there is only one person in the car, the stunt driver.
In one scene, President Douglas gives the illegal alien, Ernesto, his trench coat. In the next scene, when both former Presidents are walking along the railroad, he is holding his trench coat.
After Kramer blows out the tires on the Lexus, he and Douglas are forced to rent a Hyundai Excel, which is either a 1988 or 1989 model (flush headlights). During their escape from Long John Silver's, it switches to an '86 or '87 (recessed headlights), then back to an '88-'89.
When the Presidents get out of the truck that is hiding the illegal immigrants in it, as they walk to the back of the truck the brake lights light up, yet the driver took off and ran before the Presidents ever left the truck.
The state of the windshield after crashing into the fast-food restaurant mascot changes in successive shots.
The Presidential aircraft only become Air Force One or Marine One at the moment the President comes aboard. At any other time, even when carrying ex-Presidents, they would be identified with their serial numbers.
The helicopter used as Marine 1 is not a VH-3 - it is either a Sikorsky S-62 (civilian version) or an ex-USCG HH-52A SeaGuard with the hoist removed, and painted to look like Marine 1 (with a fake exhaust on the right side). When the helo takes off, windshield wipers are clearly visible on the windscreen - when the cockpit is shown from the inside, there are no wipers. Also, there is no rotor brake cylinder mounted on the windscreen center post. Finally, the entire Caution Advisory Panel is lit up and this would be a requirement to land immediately. Furthermore, you cannot have normal conversation in an HH-52A - you use the ICS - the InterCom System, with either helmets or headsets equipped with microphones and press-to-talk switches. And - the President always debarks from the left side of Marine 1 - this shows them leaving from the right side.
When Kramer and Douglas begin leading the White House tour, it is supposedly a ruse to get to the West Wing. However, they are clearly seen heading away from the entryway past the staircase leading to the Presidential Residence - heading towards the East Wing. Besides, they would know that from that area, one cannot enter the West Wing without either passing outside again or past a security checkpoint.
When Douglas, Kramer, and Hollis are questioning Witnaur, Kramer (Jack Lemmon) pulls a semi-automatic pistol, and a cocking noise is heard. The pistol has an internal hammer which is cocked when the slide is racked. It would not make a cocking sound.
A good deal is made of the Presidents having to appear on the South Lawn in order to show they haven't been killed in a helicopter crash, but 15 minutes earlier they were showing tourists around the White House and the South Lawn appearance was redundant. However, the purpose of being at the South Lawn appearance was to be on live cameras; the tourists did not have such equipment to prove that the Presidents were still alive.
The former Presidents joke that Rita is the only cook the White House ever had and she started with Washington. George Washington oversaw construction of the original White House, but it was John Adams who was the first to live there. However, they are clearly exaggerating about how long Rita has been there as a joke, not being factual.
When Tanner gets a call on his mobile phone during the Dutch Resistance ceremony, he acts as though he is listening to information and then relaying instructions. As he turns his head, you can see that the phone's speaker is pressed up against the side of his face, and not his ear.
When presidents Kramer and Douglas walk into the rental-car office in West Virginia, there is a Wachovia bank branch across the street behind them. Wachovia does not have branches in West Virginia.
When they were on Interstate 77 in Virginia, they pass a Welcome to West Virginia sign. In reality, The East River Mountain tunnel separates Virginia/West Virginia on I-77.
In the shooting scene in the car, President Douglas is given a summons from his ex-wife. He reads it and throws it on the floorboard of the car. When he leaves the car, he leaves the summons, which would have identified him as being in the car where a man was murdered.
When Col. Tanner enters the house of President Kramer, he addresses both of the Presidents as "Sirs." Proper protocol when addressing two superior ranking male individuals in the Government has it that you address them as "Gentlemen."