Character mistake: Before takeoff, Sully receives this instruction from ATC, "Cactus 1549, runway 4, cleared for takeoff." However, he only repeats back, "Cactus 1549, cleared for takeoff" and does not confirm the runway/his location. Flight crew and ATC always repeat instructions to make sure they're on the same page, just as he did seconds before when he and his copilot confirmed the amount of fuel required and actual fuel onboard.
Continuity mistake: During passenger boarding the screen (Flight Attendant Panel), located above the forward flight attendant seats is a newer touchscreen one, but when flight attendants are doing safety demo, it changes to the older LED push button type.
Factual error: In a scene where Sully is walking through down town NYC in between yellow cabs, one of the cabs is a 2015 Toyota, but the movie is set in 2009.
Factual error: The Space Shuttle Pavilion on the Intrepid is visible in the movie. Enterprise was only transported to the Intrepid in 2012.
Factual error: In a scene, when the airplane passes the Manhattan skyline, you may well see in the middle of the skyline the "432 Park Avenue Building" built between 2013-2015, but the movie is set in 2009.
Factual error: In the flight deck scenes, one of the engine parameters displayed is "EPR." This applies only to A320s with IAE V2500 engines. The "Miracle on the Hudson" A320 had CFM56 engines, so the parameter should have read "N1."
Factual error: When the A320 taxies out from LaGuardia there is a Continental airlines jet with scimitar winglets. These were not on commercial aircraft in 2009.
Factual error: The cockpit voice recording is highly sensitive in nature. It would never be played in front of hundreds of people like in the movie.
Factual error: The NTSB was portrayed horribly in this movie. They investigate purely on facts, not going on witch hunts like this movie implies. In the movie they tried to "second guess" and "blame the pilot." This never happens in real life.
Factual error: The plane's engines start during push-back. In real life, that is not done for safety reasons. The engines should be started after push-back.
Factual error: The movie showed the FAA HQ building. Then the next shot showed the NTSB Public Hearing Room. The NTSB is actually located around the corner in DC from the FAA. They are not in the same building.