Revealing mistake: 10 minutes into the movie, the hijacker is at the cockpit cabin door and forces the stewardess to have the captain open it. If you look behind the hijacker at the main cabin door, you can see light coming through it on the upper right each time they show him from the front. It's a sealed plane door, there wouldn't be any light coming through.
Revealing mistake: When the shot of The Pentagon is shown as word of the hijacking is made known to the State Department it's supposed to be 2:15 in the morning but there is obvious sunlight shining on the buildings making it probably dawn instead of the middle of the night.