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."
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.
After President Kramer's grandson went to play hide-n-seek, Kramer tossed aside the squirt gun he had taken from the grandson. Yet later on the helicopter he pulled the squirt gun from his jacket pocket.
When they are at President Kramer's house, his grandson wants President Kramer to play with him. President Kramer takes the boy's toy gun, holds it over his eyes, counts 100, 99, 98 then throws the gun on the sofa. He never picks it up, buy later has it in his pocket on the airplane.
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.
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.
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.
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 murder car.