The Right StuffGoofs
Continuity
When the footage of Glenn's launch is shown, the footage from the rocket looking down at the ground is actually from a Little Joe rocket launch at Wallops Island, Virginia. A characteristic orange painted tip of the stabilizing fin is clearly visible, as well as ground installations, all of which are still in use today.
When Shepard is landing on the aircraft carrier in his first scene the view from his POV shows a level approach, but when we cut to Shepard himself we can see by the ocean outside that the aircraft is in a steep turn.
Commenting on the launch and recovery of Ham the chimpanzee,
Chuck Yeager is seen wearing his flight suit with the insignia of a Colonel (eagles). Immediately subsequent to this, Yeager is seen at a party at his home where he wanders outside to look up at the moon; on the collar of his class B uniform is the insignia of a Major (gold oak leaf).
Factual errors
Yeager's NF-104 flight was portrayed as an unplanned, spur of the moment thing. Both his autobiography and the book this movie is based on imply that the flight was well-planned and the control tower would have known about it.
In the press conference scene introducing the Mercury astronauts, the astronauts all raise their hands (Glenn raises both hands) to the question "Which one of you will be the first into space"? In reality, the question raised was whether they were confident they would return from space.
During the second funeral sequence, Gordo Cooper is wearing decorations on his service dress uniform denoting service in the Korean War. In reality, Cooper was the only member of the "Original Seven" who was not a combat veteran.
Incorrectly regarded as goofs
When Yeager makes the first supersonic flight, we see the plane's Machmeter going offscale because it only reads up to Mach 1. Although this seems completely silly because the plane was always intended to fly supersonically, it is in fact what happened.
Near the beginning of film, after the civilian pilot demands $150k to try to break the sound barrier, the group that asked him approach Yeager to see if he will do it. They get his attention by calling "Major" to him, but Yeager is wearing a Captains insignia at the time.
When the officer approaches the table at which Jack Ridley, Chuck Yeager and two women are sitting, it is actually Ridley that properly addresses the officer as Major. The officer then says "Say there, Yeager" to get Yeager's attention, to which Yeager replies, "Sir."
The launch on May 15, 1963 of "Gordo" Cooper, is portrayed in the film by what looks like a Mercury Redstone launch vehicle, when this was only used for the first 2 (non-orbital) Mercury missions (and some non-manned tests). This mission actually used the Atlas LV-3B launch vehicle which looks quite different. However, the footage used shows indeed the Atlas rocket. The confusing white color of the rocket is not paint though but ice, formed on the rocket's surface once it was filled with an extremely cold liquid oxygen shortly before take off.
Revealing mistakes
According to the serial number seen on the canopy of Yeager's F-104, that particular aircraft was built as a G model, in Germany by Fokker Aircraft, for the Luftwaffe in 1963. It flew in USAF colors at Luke Air Force Base (near Glendale, Arizona) from 1964-1966. (Interestingly, this exact same aircraft was totally destroyed in a crash 5 miles west of Aguila, Arizona on 3 March 1966. The German pilot successfully bailed out.)
Towards the end of the movie when Chuck Yeager ejects from the NF-104, you can see the Cessna that carried the stunt man in the upper part of the screen.
The shot of the B-29 starting its engine shows a small air intake immediately behind the propeller, and is clearly painted black along the bottom half of the engine cowling and underside of the wing. However, the shot of the B-29/X-1 combination taking off for the sound barrier flight is archival footage of a B-50 carrying an X-1. The B-50 was an updated model of the B-29 with improved engines. The updated engines have larger air intakes set much farther behind the propellers. Also, the B-50 shows no black coloring, instead it's unpainted aluminum.
Miscellaneous
At the end of the movie an ambulance is racing to get Chuck Yeager after bailing out of the NF-104. The ambulance is seen racing through the desert of a restricted Air Force Base, and there is no other traffic for miles, but the driver still has siren activated (A siren, as pointed out by previous readers, that was not available at the time.) Who was he trying to warn?
During the barbecue scene early in the morning, the new test pilots see and discuss the D-558-2 Douglas Skyrocket the see in flight. The Skyrocket was a combination jet and rocket-powered aircraft, which flew for the final time in 1956. The aircraft used for the film, was a Hawker Hunter, dressed up to appear as the Skyrocket. A noticeable difference in the aircraft is the position of the aircraft's intakes.
At the press conference introducing the Mercury Seven astronauts, Malcolm Carpenter's first name on the place card is misspelt as Malcom.
Anachronisms
The call sign of the X-1 that crashes before Yeager's flight is "Whiskey Kilo Two." "Whiskey" and "Kilo" represent W and K in the NATO Phonetic Alphabet, which the U.S. Armed Forces adopted in 1956. Yeager's flight took place in 1947, when the armed forces used the Joint Army-Navy Phonetic Alphabet, in which "William" and "King" represent W and K.
When the footage of Gagarin in space is shown, the soundtrack is of another Russian cosmonaut, Alexei Leonov, saying that the Soyuz spacecraft is ready for the merging with Apollo (which took place in 1975).
When Alan Shepard walks between the cheering crowd upon landing on the aircraft carrier, some sailors have beards, something the Navy allowed for a few years in the 1970s and early-'80s (when the film was being shot) but unheard of in the early-'60s.
Audio/visual unsynchronised
When Yeager stalls the NF-104, "engine restart" sounds are heard before he actually moves the toggle switches.
Errors in geography
After the awards ceremony, the Grissoms return to their motel on the beach in Florida. Certainly this is near Cape Canaveral on the East Coast. But when the newsmen swarm outside their window, we can see the sun just above the ocean horizon behind them. On the east coast, this would mean it's just now dawn.
Character error
At the press conference, astronaut Scott Carpenter, whose first name is Malcolm, has his nameplate misspelled as 'Malcom'.