When Taraji P. Henson signed on for the lead role, she met with 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.
Astronaut John Glenn did specifically request that Katherine Johnson review all of the calculations for the Friendship 7 mission - (his dialogue in the film based on NASA transcripts*) - before he could be confident enough to proceed, but which in reality occurred a few weeks before launch: not as depicted in the film whilst awaiting the launch. And Katherine Johnson's calculations (more realistically) took (just!) three days to confirm. (*Director's own DVD commentary information.)
The issue with the bathrooms was not something Katherine Johnson personally experienced. It was encountered by Mary Jackson instead. In fact, it was this incident, as a result of Jackson ranting to a colleague, which got her moved to the wind tunnel team. Johnson was initially unaware that the East Side bathrooms were even segregated, and used the unlabeled "whites-only" bathrooms for years before anyone complained. When she simply ignored the complaint, the issue was dropped completely.
Paul Stafford (Jim Parsons) and Vivian Mitchell (Kirsten Dunst) are not based on real people. Instead, both characters are composites of different team members who worked at NASA, intended to represent the dismissive attitudes held by some of the white co-workers during this period.