These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Ending Fatigue: Just when you thought the film was gonna end after Korshunov and Radek dies, MiGs loyal to Radek launches to shoot down the plane only to be stopped by friendly F-15 Eagles. Then, it turns out the plane is almost out of fuel and thus, unable to land. Marshall pilots the plane to the Caspian Sea and the USAF sends in an MC-130 to evac the president and everyone else via zip-line, but then Gibbs tries one last attempt to kill him, but fails to do so as the plane crashes, taking him with it. The film finally ends for real afterwards.
Ensemble Darkhorse: William H. Macy makes Major Caldwell a very likeable character, making many viewers to feel upset when he dies.
Harrison Ford played Jack Ryan in two movie adaptations of Tom Clancy's Jack Ryan novels. The novel published a year before the movie shows the character dealing with becoming the US President.
Honor Before Reason : The military leaders loyal to Radek launch MIG's to shoot down Air Force One after he and Korunsov are killed. Assume the President and his family are all killed, especially after overcoming the terrorists. What then? Assuming their republic isn't made a crater, it is easy to imagine sanctions so ferocious and long-lasting that reaching the Stone Age might be a pipe dream, likely extending to anyone dealing with them. No matter who was POTUS in years to come, this would be enforced basically forever. So, Comrade? Didn't Think This Through, much?
Rooting for the Empire: Some viewers feel at least a little sympathy for Radek desperately fleeing for his life while being machine gunned by faceless guards. The fact that we don't actually see what his crimes are helps it.
It is mentioned at the beginning that the President had been to the Red Cross camps and seen the thousands hurt under his rule.
So Cool It's Awesome: The idea of the President of the United States fighting back against terrorists. Many critics say the film is no cinematic masterpiece, but the absolute ridiculousness of the scenario makes the movie fall under this trope.
Special Effects Failure: The crash of the eponymous aircraft. The 1997 CGI looks like something out of a video game from that same year. Which is too bad because the effects so far had been fine against the night background, and only become obvious when the sun rose in the movie.
Tear Jerker: Most notably when the President is given a Sadistic Choice between the life of an innocent woman and his chance of saving everyone else. Ivan turns on the intercom so everyone on the plane can hear her plead for her life, right up until he shoots her, and we see the other hostages either close to breaking down or openly sobbing.
What an Idiot: Terrorist Sergei apparently doesn't know what explosive decompression is. To get through a locked door he jams a fire extinguisher in the handle and shoots it. On a plane. This results in at least five people (including a restrained terrorist) getting sucked out of the plane (although we see three people have chutes safely opened). And the President almost fell out. Unfortunately, Sergei isn't one of them. This also leads to the explosion of the tanker plane that was refueling Air Force One at the time, and could easily have killed EVERYONE if not for the pilot's quick thinking.
Also Agent Gibbs. Does he really think he is going to be guarding any more presidents even if he didn't leave the president behind on a doomed plane?