Factual error: When the aircraft window is shot out, depressurization of the plane occurs shortly after the door of the plane blows off. When depressurization occurs, the pressure in the fuselage drops. Why would the door blow-out now when it held before with higher (normal) pressure?
Factual error: When the large airliner is brought down at the the small, regional airport, a huge movable stairway is rolled up to the aircraft so that people can disembark. There is absolutely no reason why a stairway designed for major jet aircraft would be sitting at a small airport that didn't even have runways long enough to accommodate such large airplanes.
Factual error: Just after Ranes shoots a hostage, when in the standoff with Cutter, the pistol (a Beretta semi-auto) is shown uncocked, which wouldn't happen normally since the movement of the bolt after the shooting to eject the capsule also cocks the guns automatically.
Factual error: The L-1011 lands at the small airport and the hijackers demand fuel. When the fuel tanker shows up with the fuel, the fueler opens the fuel panel and puts an 'overwing' nozzle up inside the fuel panel. This type of nozzle would only be used if the fueler was on top of the wing filling the wing through a small gas-cap type of fueling point.
Factual error: First, when Raine fires his gun and blows out a window, it causes explosive decompression which results in a door being blown off. It has been proven (Discovery TV's "Mythbusters") that explosive decompression does not result from a gunshot hole. The plane would, of course, lose pressure, but slowly. Even explosive decompression would not rip a door off its frame. Second, with the plane decompressed, Cutter and Raine (and everyone else) would have passed out within 15 seconds from hypoxia. It's funny that not a single person in view of the cameras actually put an oxygen mask on. Third, as soon as decompression was detected, any well-trained pilot would have put the plane into a dive immediately to get it below 10000, so that passengers wouldn't die. It is interesting that even at the end of the fight, as we see Raine falling to the ground, the plane is still flying straight and level at altitude.
Answer: The plane would not be able to take off from that small airport.