Factual error: In the Vostok launch clip, it shows Yuri Gagarin lifting off at night. The actual liftoff occurred during the day, at 9:07 AM (Moscow Time). Plus the rocket shown in the launch clip isn't even a Vostok rocket, it's a later variant used by the current Soyuz spacecraft. (Evident by the color, and on the top of the rocket is a Soyuz escape system).
Continuity mistake: When John Glenn's Atlas rocket is shown both before liftoff and as it is lifting off, a hodgepodge of stock rocket footage is pieced together. Some Atlas rockets are white, some unpainted. A camera attached to the outside of the rocket looking backward shows fins at the base of the rocket. The Atlas rocket had no fins. It also shows the rocket oscillating wildly on its axis as it ascended, something no normal manned rocket would do.
Continuity mistake: When the astronauts are putting on their space suits, Glenn gives a speech about morality. While Shepard rebuts Glenn's speech the space suit on the left of the clothes rack changes position throughout the sequence. It is at time at the right side of the section of the rack, turned toward the camera, turned away from the camera, moved close to the middle of the section of the rack. There is also an empty hanger that appears later in the shot when it was not there beforehand.
Continuity mistake: After Gus Grissom and his wife discover their refrigerator has been filled and they begin fighting, reporters show up outside their balcony. In Gus's preparation to meet with the press, he buttons up his blazer, then turns around to face the cameras. The next camera shot shows from outside the apartment and Gus buttons his blazer once again. He had already buttoned it up once and did not have time to unbutton it.
Factual error: The first supersonic flight of the Bell X1 was flown in total secrecy. The news of the flight was not even released to the press until January 1948, three months after Yeager broke the sound barrier. Yeager's wife and the owner of the local bar were most certainly not present.
Factual error: At the scene describing the test flights of the Bell X-1, they show a flight that ends with the crash of the plane. This is completely untrue. There was no such crash of any Bell X-1 plane prior to the record breaking flight by Chuck Yaeger on October 14, 1947. There were 3 Bell X-1 planes built. The first is the famous record breaker plane. It was retired on May 12, 1950. It is on display in the Air National Museum in Washington DC. The second flew until October 23 1951 when it was rebuilt as X-1E. The third X-1 started flights only on July 1951 and blew-up on the ground on November 9, 1951.
Character mistake: In the scene where the pilots and their wives are barbecuing, a jet flies overhead. One of the pilots says, "Hey look at that" and another says, "Yeah that's the D558 phase II, Scott Crossfield". In fact it is not the D558 phase II. The D558 phase II is the Douglas Skyrocket. Only three Skyrockets were built, in both jet power and rocket power, and they do not have wing air intakes like the jet shown flying by. Only the jet powered Skyrocket had air intakes and they were located on the lower side of the fuselage just above the front landing gear.
Continuity mistake: In the scene at Pancho's bar, during the pudknocker conversation, Panchos' hand holding a cigarette changes in each side of the shots.
Other mistake: When the astronauts are in front of the space craft and have reached terms with the scientists, Carpenter whistles then waves the press in. One of the pressmen says "Look, Glenn's waving us in!", he should have said Carpenter. The astronauts were all very high profile persons in the press and would be easily identifiable and the press members were top notch professionals so it is not considered a character mistake.
Revealing mistake: In the scene in which Alan Shepard is about to land his jet on the aircraft carrier, the plane seen from the outside is a single-seat A-4 attack plane. But inside the cockpit actor Scott Glenn lowers his sunshade, and reflected on the shade can be seen the wings of a two-seat jet trainer, the T-33A.
Continuity mistake: When Gordon is in the bathroom stall preparing to produce a sperm sample the camera pans down to the bottom of the stall. We can see the legs of the people in two of the stalls, Gordon and one other candidate. After Gordon says "Ok Glenn, I know that's you", the scene jumps a little. The belt of the astronaut to the left moves where the shots were joined. This was obviously two different shots that were spliced together at this point.
Continuity mistake: When Alan Shepard is at the presentation ceremony with President Kennedy after his first flight in to space, he has a medal on his suit jacket in a shot at the beginning of the ceremony, then you see Kennedy pinning the medal on him at the end of the ceremony.
Factual error: During the sequence of rocket malfunctions, the very last malfunction actually happened, but it is shown incorrectly. In the movie, an Atlas rocket refuses to launch, and the Mercury capsule atop it ejects its parachute with a champagne-cork pop. The real malfunction occurred during an early unmanned Mercury test flight, using a Redstone rocket. Instead of the rocket lifting off as planned, the Mercury capsule's launch escape tower fired, leaving both rocket and spacecraft on the pad. The capsule's parachute did eject, and threatened to pull the rocket off the pad.
Factual error: The story line suggests that Yeager broke the sound barrier on his first flight in the X1. In fact it was only after a series of flights that edged the speed up gradually that Yeager exceeded Mach 1.