The movie is mostly accurate except the negative villain-like portrayal of NTSB (National Transportation Safety Board).
The movie is based on Highest Duty: My Search for What Really Matters. It is a memoir written by Chesley Sullenberger and Jeffrey Zaslow describing the events of US Airways Flight 1549. Of those two, Chesley Sullenberger (Sully) was the Captain of the flight 1549.
The fact that the movie is based on an actual memoir by Sully himself establishes accuracy of the main premise/plot of the movie and the actual incident as the happened. Additionally as Captain Sully said in his statement:
“The story being told came from my experiences, and reflects the many
challenges that I faced and successfully overcame both during and
after the flight. I was involved in the development and am thrilled
it’s being brought to the screen.”
Talking about the actual landing and the whole incident, the movie "pretty accurately" captures what happened that day, as told by the survivors themselves.
If you are interested to know more about the actual incident - a survivor did an AMA session on Reddit answering various questions and describing the entire experience.
But just portraying this incident in one linear fashion would have almost made it seem like a documentary. Suspense and the I-was-on-the-edge-of-my-seat factor was missing in the film. So director Clint Eastwood wanted to bring in a villain in the movie.
As a result they made the NTSB (National Transportation Safety Board) villain and portrayed them as prosecutorial and closed-minded. The federal investigators who conducted the inquiry into the flight contend that “Sully” tarnishes their reputation. The investigators, including Robert Benzon, the now-retired leader of the inquiry along with the other investigators said
the scriptwriters heightened the drama by adding a level of testiness
to the N.T.S.B. investigation which is unfair and inaccurate.
But interestingly enough, Allyn Stewart, a producer of movie has responded to this saying:
The story is told through the experiences of Jeff and Sully, and so
they felt under extreme scrutiny and they were
If you are interested more in the investigation and the final verdict you can read the full transcripts of its public hearing - Part 1, Part 2, Part 3,
An example of inaccuracy
Remember how in the movie Captain Sully asks to add those 35 seconds as a "human factor" for next simulation? In reality, investigators were the ones who had asked to do that
In reality, investigators first asked simulator pilots to attempt
airport landings immediately after engine loss to establish the bounds
of practicality. Notably, even with the benefit of perfect hindsight,
barely half of these optimal test runs made it back. And then the
investigators – not Sullenberger – asked a pilot to wait 35 seconds
before attempting an airport return. That flight didn’t make it.
Consequently, the NTSB was unequivocal in its declaration that the
Hudson was the right call.