When Taraji P. Henson signed on for the lead role, she met with the real-life Katherine Johnson, who was 98 years old, to discuss the character she was about to portray. Henson learned that Johnson had graduated from high school at age 14 and from college at age 18, and was still as lucid as anyone years younger. After the film was screened for Johnson, she expressed her genuine approval of Henson's portrayal, but wondered why anybody would want to make a film about her life.
The issue with the bathrooms was not something Katherine Johnson experienced, but rather lived by Mary Jackson. In fact, it was this incident that resulted in Jackson ranting to a colleague which got her placed on the wind tunnel team. Katherine Johnson simply refused to use colored restrooms.
One of the ways that Katherine experiences workplace discrimination is when her coworkers require her to use a separate coffee pot. Whenever the office's coffee area is shown, the brand of coffee that they use, Chock full o'Nuts, is also visible. The use of this brand in the context of segregation is historically interesting, since in 1957, Chock full o'Nuts was one of the first major New York corporations to hire a black executive as a corporate vice-president--and the man they hired, retired baseball legend Jackie Robinson, had himself been the first person to break the color barrier in professional baseball.
The set where IBM genius Dorothy Vaughn's house was filmed (where the 3 ladies played cards and danced) was actually an historic house in Atlanta where civil rights legends Ralph Abernathy and Martin Luther King Jr. met.
The actual working relationship between the engineers and women was not as hostile as it appears in the film. While there were clearly racial issues at play, the majority of the engineers were able to work with the computers with no issues.
On the day that the scene was filmed in which Paul Stafford (Jim Parsons) is speaking to the NASA engineers in the Space Task Group office about needing to develop the math for re-entry, there was an extra face in the crowd. Mark Armstrong, son of Apollo 11 astronaut Neil Armstrong, had been invited by actor Ken Strunk to have a cameo appearance in the scene, and joined the other actors representing the NASA engineers.
Colors were key to setting the films mood. "Cold" sets at NASA - where calculations took place - were filmed in sterile whites, grays, and silvers; sharply contrasted against the "warm" sets of Kevin Costner's office and the ladies' homes.
The trivia item below may give away important plot points.
The film accurately portrays what was believed to be a heat shield failure upon re-entry. The film did not provide further explanation, but it turns out the heat shield was functioning normally and it was the indicator itself that was faulty. The flaming debris seen upon re-entry was not the heat shield but the retrorocket pack. At the time, however, John Glenn had no way of knowing that.