Continuity mistake: When Sully is boarding the aircraft the forward galley has catering in atlas boxes with no flight labels on, when they are done with the demo and the cabin crew secures the galley it has changed to a galley with doors and a boiler. (00:26:27 - 00:30:00)
Other mistake: When Sully gets on the plane, his jacket / coat fall off the luggage he is pulling. Even the flight attendants do not realised what happened. (00:27:28)
Factual error: If you look at the takeoff seen you can see an American Airlines 737 800 in the new livery despite this move taking place before American having their new livery.
Factual error: When Sully decides to land in the Hudson River, the aircraft is approaching the George Washington Bridge the Ground Proximity Warning System advises to the pilots "Obstacle, Obstacle." This is correct; however, after the aircraft clears the bridge, the system then announces "Clear of conflict." This is incorrect, because the GPWS doesn't advise when clear of terrain. The Traffic Collision Avoidance System advises when clear of conflicts, which is only between aircraft.
Continuity mistake: A girl in blue jumper is on the right of the passenger with golf hat. Next scene she is on the left of the passenger and his elderly father on a cell phone. (00:50:09)
Factual error: A (white) iPhone 3GS is shown after passengers are rescued by the American Red Cross, but that iPhone model was only presented during the summer of 2009, whereas the landing on the Hudson happened in January. The iPhone 3GS was the first iPhone also available in white.