Corrected entry: 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.
Corrected entry: 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.
Corrected entry: The movie shows American Airline's new livery that was revealed in 2013, four years after the miracle on the Hudson happened.