In the Book
In the Movie
After working six months for Henry Pearson, Vanghan demanded that Pearson promote Katherine Johnson or send her back to West computing. Pearson offered Johnson a permanent position in the Maneuver Loads Branch.
This does not happen. Katherine works in the office of Al Harrison the entire movie.
Katherine kept her graduate school math textbooks at her desk for ready reference.
She does not.
Katherine's 1st assignment was to help evaluate the crash of a small Piper airplane. This aided in the discovery of vortexes from larger aircraft.
Her first assignment was to check the numbers of the engineers working in her office.
Katherine Johnson never used the colored restrooms at Langley even after she found out they existed in her section. She also brought her lunch to work in a bag like the engineers and avoided the segregated cafeteria.
She walked a long distance to use the segregated restrooms which kept her out of the office at time leading to friction between her and the boss.
Katherine's fair skin nearly allowed her to pass as white although she never tried to.
Taraji P. Henson is much darker than the real Katherine Johnson.