Though on takeoff the plane is shown as a Boeing 737, it is a Boeing 747 for the remainder of the film. The interior cabin of the plane is shown to be a coach section and first class, in a narrow body configuration. This would be correct for the 737, but not for a much larger 747.
Over a full minute passes from the time the plane is shown leaving the ground to when the pilots are advised they must stay below 1,300ft- their autopilot control panel shows an indicated altitude of under 900ft. A 747-8 would be likely be around 2,000-2,500ft at this point on climbout.
Numerous characters refer to the jets escorting the hero plane as 'F-16s', despite an F-16 only appearing in one shot- preparing for takeoff in a mountainous environment that looks like Nellis AFB in Nevada. The planes used as escorts are F-18 fighters which are used by the US Navy, not the Air Force.
Despite the hero plane being a Boeing 747, most shots of the flight deck and of flight instruments are those of a Boeing 737. One shot shows two display screens mounted in a brown panel, which would be correct for the 747. Near the end of the film, a hand is shown adjusting the thrust levers, but these are from a twin-engine Airbus.
Despite the cockpit windows being riddled with gunfire and a heroic ex-army soldier tossing luggage from a cargo hatch mid-flight (an impossibility in its own right), the plane maintains pressure and the passengers do not seem disturbed at all.