Continuity mistake: After the hijackers have taken over the plane, the blond flight attendant's hair, styled in a French Twist, keeps changing from messy (presumably from the chaos) to as smooth and neat as when she boarded the plane. She's never offscreen long enough to have simply fixed it. Not until the passengers revolt does it remain disheveled.
Audio problem: When auditing the recording of one of the first hijacks, the FAA reviewer rotates the tape reels back and forth in order to find just the exact words from the hijacker. As the sounds play, the reel moves barely half a turn, but the reviewer rewinds it more than one revolution, not nearly returning to where that sound would be.
Factual error: In a scene in New York's air traffic control tower (I think the one where they show the second plane hit the south tower of the WTC), there is a man wearing a black lanyard around his neck that says "Transportation Security Administration" on it. The TSA was formed shortly AFTER the events of 9/11 thus he should not be wearing it.
Continuity mistake: In both the exterior shots during the film and in real life, the Boeing 757-222 (N591UA) operated by United Airlines is shown to have 2 doors forward of the wing. In the interior shots, the front door is shown, but between the first class cabin and the economy class cabin, there is just a partition, no door.