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.
Suggested correction: The NTSB is, like any other organisation, is run by people with their own biases and imperfections.
This goes way beyond biases and imperfections. Sullenberger himself was disturbed by the way the NTSB investigators were depicted. Having reviewed an early draft of the script, he asked that their names be removed from the characters. According to Hanks, Sullenberger felt that the NTSB investigators were not prosecutors, and it was not fair to associate them with changes in the story to depict "more of a prosecutorial process." The film's version of the investigation is wildly inaccurate.