Continuity mistake: In the beginning of the movie when the car is broken down you can see either a whole bunch of cows are in the field through the passenger window. When Dorothy starts the car with the screwdriver the cows are gone. (00:03:10 - 00:05:54)
Factual error: The signs in the hallway are made of blue plastic. Not in 1961. They became common later. (00:09:35)
Factual error: When character Mary Jackson was appealing to Judge in court and sweet-talked him by mentioning his college that he graduated from George Mason, George Mason didn't exist until after 1957 and the movie setting was 1961-1962, which wouldn't be enough time for the character to graduate and become a judge by then. (01:00:00 - 01:05:00)
Continuity mistake: When Katherine is working out the math in the conference room for John Glenn's start off to the Bahamas there is no chalk or pencils on the desk, but they reappear when Al Harrison hands Katherine the chalk. (01:23:40)
Factual error: In the conference room Katherine is at the board working out of the re-entry figures. She begins by converting 17544 mph to 25371 feet per second. The correct answer is 25731, an error of just over 1 percent in the first line of her calculations. She persists with the error but, contrary to the calculations she's presented, she gives the answer that she would have obtained had she not been working with the wrong figures. She then says that her obtained answer converts to 2990 miles, which it doesn't. (01:34:50)
Factual error: In the conference room scene Katherine presents the landing point, orally and in writing, as 5.0667° N and 77.33° W then indicates this is the target landing point in the area of the Bahamas "give or take 20 square miles." However, this latitude and longitude is actually on the Pacific coast of Colombia - about 1300 miles from the Bahamas and on the other side of Central America. (01:36:00)
Factual error: In the background towards the end there is a Mercedes Benz W108 that was not built before 1965. (01:42:45)
Continuity mistake: When Atlas is launched, Catherine stands in the control room next to the person who has radio contact with Glen. There are three different takes from the same camera angle, and in the last one, Catherine is not standing next to the radio person. It's only a few seconds apart. (01:44:02)
Continuity mistake: In the final scene between Harrison and Katherine. Her pearl necklace starts tucked into her dress, then out while she says "You too, Mr. Harrison", and then back in. (01:56:36)
Character mistake: A TV news announcer describes Alan Shepard's first manned launch into space as him being lifted to "an altitude of 116 miles per hour." That's not an altitude, that's a speed. It should have just been "116 miles."
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: In one scene in the car (a 1957 Chevrolet), someone turns on the radio. The sound from the radio is heard immediately. This would only happen in a transistor radio. The radio in that year Chevy was a tube radio, and would need time to warm up before any sound was heard.
Factual error: The movie takes place in 1961 but the police car escorting the women to work is a 1964 Galaxie 500.
Continuity mistake: When Katherine realises she can use Euler's Method to calculate how to bring John Glenn safely back to earth, she is seen wearing a wristwatch when she's at the chalkboard. The watch is not on her when she leaves to get a book about Euler's Method. It reappears when she's back at the chalkboard.
Factual error: The truck that drives John Glenn to the launch pad is an M939 series 5 ton, which did not go into service until 1982.
Factual error: The eight stripe IBM logo is shown on a portfolio. That logo did not exist until 1972.
Factual error: During this era (I was there), nearly everyone (myself excluded) smoked like chimneys, and engineers in the office scene were no exception. All depictions of them laboring over their slide rules should have, realistically, been seen through a thick haze of cigarette smoke.
Revealing mistake: When the ladies are being escorted by the police to NASA, their Chevy is in park.
Factual error: When they are watching the video of Yuri Gagarin's space flight (April of 1961), the announcer describes the time as "UTC." The official abbreviation of UTC and the official English name of Coordinated Universal Time was not adopted until 1967. They would have described it as "GMT" (Greenwich Mean Time).
Continuity mistake: In a scene where Katherine is writing on the big chalkboard, calculating the reentry spot (or something similar) for Friendship 7, her left hand is shown with an engagement ring. Her boyfriend doesn't propose until after this scene. You only see it for a second.