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: During the flashback to the F-4 flight emergency, the visuals are inconsistent with the dialogue: they are approaching runway 21, which has a runway heading of 205 to 214, and the visuals before the dialogue shows them lined up with the runway. The dialogue of Sully's back seater is "Heading 020, five miles out, sir." This is 170° away from the runway heading, almost the opposite direction. (00:41:31)
Continuity mistake: A passenger has a New York Waterways life jacket long before the Thomas Jefferson (first New York Waterways ferry to arrive) has arrived. (00:49:15 - 00:55:14)
Other mistake: During the F-4 emergency flashback, Nellis Tower has cleared them to land on Runway 21, however the runway is marked 22. (00:40:57 - 00:42:05)
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.
Factual error: When Sully approaches the airport vendor for a sandwich we see a souvenir orange New York license plate reading "Times Sq." New York didn't introduce the new orange plates until April 2010.
Factual error: When Sully buys a sandwich, one of the magazines in shot is the September 2015 issue of Jaguar World. The scene is set in 2009. (00:27:00)
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.
