When Jack shoots Nicole through the wall, as her dead body slides downward, a blood stain is visible on the wall. But as the camera follows Jack down the stairs to inspect the body, the stain is gone.
Michelle Dessler says Air Force One has four fighter escorts, but Chloe's radar screen back at CTU shows five.
Anderson takes off in the stealth fighter. As he lifts off he calls departure control and states, "Bravo-three-niner in the air, heading 552." This is impossible. There are only 360 possible headings based on compass directions.
The F-117 is not equipped with radar. If it used radar it would be traceable by its signals. Though it has a forward looking infrared system. Furthermore it's unlikely that it would have been equipped with air-to-air missiles on a standard training mission (it's not a fighter, but a bomber).
In addition to the F-117A no being equipped to fire missiles, the aircraft was prepped for a training mission and would not have live munitions. Air Force 1 is equipped with the best infrared and radar countermeasures which would make a hit from a missile unlikely.
Chloe tells Tony Michelle was posted in Seattle while he was in jail. Tony was sent to prison, not jail.