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 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)
Factual error: The IBM arrives on several pallets with the parts on the pallet fixed with stretch foil. This foil became common in packaging at least ten years later. In the 60s sensible equipment was crated and one should have seen huge wooden boxes.