After the crew has gotten back control of the plane and its on its way to Dullas Airport, the exterior shots of the plane has the missing engine in at least 2 exterior shots.
After cutting off the courier's hand to get the briefcase the knife is covered with blood but when the hijacker is hiding the case the knife is clean.
The fighter pilot is cleared to fire a missile towards the plane because they are in an open area. But when the missile goes off track it hits a tower in the middle of the city.
The same shot from above with plane below is shown at least three times with the exact same area of terrain.
In 52nd minute when the plane flies sideways between the two buildings, the hijacker in the cockpit doesn't fall down.
Dulles International Airport, not Dullas.
After the plane has landed safely in the Potomac River, the pilot states that they have landed in the Hudson River.
The pilots are struggling physically with the controls as if they were fighting cable resistance, but a sophisticated plane would be fly by wire and they should not feel the physical effects.
The door into the cargo hold is a toilet door; complete with coat hook on the 'inside'. The lock and 'vacant/occupied' sign have been taped over with grey gaffer tape.
After the plane lands in the river, you can see the Washington Monument intact in the background. The Monument had been destroyed minutes earlier.