Continuity mistake: When the girl goes down in the plane's elevator, you can clearly see the phone to her left (our right) has no light. In the later parts of the movie the phone becomes a very significant tool and now has a light on it. (00:12:03)
Continuity mistake: When you see Rat pull himself vigorously along the wire upside down, there is no equipment on his head whatsoever, although in the very next shot when he lets himself down from the wire, he has his infrared goggles attached to his forehead. (01:12:35)
Continuity mistake: When Grant goes down to the main cabin and is looking around for the sleeper, the fringe of his hair goes from up and pushed back to all hanging down without him touching it.
Continuity mistake: Near the end of the movie, when Grant takes control of the airplane and lands on his second try, you can see the inner engine on the left wing (right to us) fall off and catch fire after impacting with the smaller parked planes. In the next shot, which happens quickly, you can see the engine is still in place and not damaged at all. In the next shot, it's gone again and the wing is on fire where the engine was.
Continuity mistake: John Leguizamo's character is protected by his bullet-proof vest when David Suchet shoots him. Despite this the vest would still be damaged, yet when Leguizamo is seen lying face down the back of his vest is unmarked.
Continuity mistake: The second time David Grant (Kurt Russell) is calling the stewardess on the phone he keeps pressing the button. The movie makes it seem like every time he presses the button, the light blinks. You can clearly see him stop pressing the button but the light still blinks.
Continuity mistake: When Louie sees Grant walking Jean down the main cabin they are already at the set of seats they think the sleeper is sitting in but after about 10 seconds of walking they reach the same seats again.
Continuity mistake: Mr Grant is at a dinner party wearing a tux. Then he is in a meeting, and told they must fly within an hour, but it is during the day.
Suggested correction: Everything you mentioned happens during daytime hours. When we see the establishing shot of Washington DC, the sun is up. Although Grant is in a tuxedo, it is not a dinner party. In fact, while he is talking to the woman, it is daylight outside. He then rushes off to the Pentagon, and then to the airfield, all which happens during the day.