Factual error: The movie takes place in 1961 but the police car escorting the women to work is a 1964 Galaxie 500.
Factual error: The eight stripe IBM logo is shown on a portfolio. That logo did not exist until 1972.
Factual error: The green car that the 3 ladies are always in has a shot where you can see the brand of tires being a Hankook Optimo. This was in 1961 and these radial tires didn't exist yet.
Factual error: The truck that drives Neil Armstrong to the launch pad is an M939 series 5 ton, which did not go into service until 1982.
Factual error: When Colonel Jackson comes to town to organize a National Guard unit, he is wearing the Army Green military uniform. It only has the branch insignia (infantry) and the US lapel. It has no name tag, no shoulder insignia showing what unit he was assigned to, no shoulder unit crests and no award ribbons. A person with that rank must have been in the Armed Forces at least 16-18 years and no ribbons?
Factual error: In at least two places in the film an IBM Selectric is used. They are: (a) A room at the beginning of the movie where typewriters are shown; (b) Near the end when Katherine Johnson (Taraji P. Henson) is typing up her report. The Selectric was introduced on July 31, 1961 (the year most of the movie takes place). It is impossible for it to have been used during the first scene as that takes place prior to Shephard's flight, which was on May 5, 1961. Glenn's flight in Friendship 7 took place on February 2, 1962. So the Selectric may have been used by Johnson at that time, but it is extremely unlikely. IBM had expected to sell 20,000 in the first 6 months and had orders (not deliveries) for 80,000 of them by the end of 1961. They were rare. NASA would not have gotten one, as law offices and similar business were IBM's bread and butter.
Factual error: When John Glenn is in the van being transported to the launch pad, the van is being escorted by a police vehicle with Virginia markings. (The launch pad is in Florida).