The NASA weather reporter indicates sky conditions will be "CAVU" (clear and visibility unlimited) for the launch. When Roy arrives at the space center on launch day though, it's an overcast sky. Just minutes later, at the base of the rocket, it's mostly sunny with a few clouds.
All through the film, during the various shots of the rocket launch and flight, the NASA stock footage that's used alternates between shots of a Saturn I vehicle and and Saturn V vehicle.
When Fleming respools the capsule's programming tape, he accidentally has gotten the peanut butter mixed in with it. The tape reels are so clogged, they cannot play. Later, when Fleming looks out the capsule window at Hawaii, the tape reels are seen in the background running normally. The peanut butter then returns in subsequent shots.
When Roy looks into the centrifuge room, it is brightly lit. But when he tries to close the door he accidentally opened, everything is dark beyond the door.
The three Greyhound buses Roy boards during the film all have the same number.
Roy's astronaut suit displays an American flag with 48 stars instead of the correct 50.
When Roy is in space, he's shown doing somersaults while weightless. One of NASA's ground personnel who is monitoring him reports that "he's rotating at a rate of 360 degrees per second," which means that he'd be making a complete rotation every second. His true speed of rotation is nowhere near that fast.
When Roy sees his Pa and friends from back home coming to visit the space center, he leaves the buffer, and it's still running on its own. A buffer has a 'dead-man's switch' that turns it off when it isn't being held.
In the first airport scene, the airliner's right-hand engine is started with no apparent effect on the passengers standing behind it. In reality, they would have been enveloped in a cloud of blowing smoke, dust, and loose articles; also, men's hats would have blown away.
The space capsule Roy is in is far too large. Mercury and Gemini capsules had small interiors, without the room for the extensive floating around that Roy is seen doing.
When Roy arrives at the Johnson Space Center in Houston, he goes to the personnel office, but it has a sign out front that says it's closed from 12PM until 2PM; he then goes to the cafeteria to wait. However, his shadow is very long, indicating that it is not the early afternoon but late afternoon or early in the evening.
When Roy gets into a capsule mock-up (labeled "Environment Simulator") for a photograph, the hatch window is clear glass. When the hatch is closed, the window is now opaque "sugar glass," which Roy shatters in order to escape from the mock-up when he is unable to reopen the hatch.
When in the space capsule, the strings holding the microphone, the doll, the crackers, and peanut butter are visible. When Roy is floating around the capsule, the strings holding him are also visible.
When where Roy (Don Knotts) accidentally opens the door to the centrifuge and is subject to high winds pushing him down the hall, two shirts and a pair of boxer shorts can be seen attached to a single wire that is quickly pulled down the hall.
There is no desert in the vicinity of the NASA space center in Houston; the area has a humid coastal climate.
Roy lives in the town of Sweetwater, in the state of Missouri. When Roy goes to the airport to fly to Houston, there are mountains in the background rising thousands of feet in the air. The highest elevation in Missouri is 1,772 feet above sea level, but the peak only rises 512' above the surrounding terrain.
It's unlikely that the picture of Roy standing with the astronauts would have been released to the press. The photographer should have noticed him standing there, and if he didn't, the picture would have been cropped when printed to remove him.
Roy is said to be an only child, but he has four nieces.
Hawaii had become a state about 8 years before this movie was made. Perhaps no one knew how to properly pronounce some of the more obscure Hawaiian names, but when Roy is orbiting over Hawaii, Fred Gifford (Leslie Nielsen) says he is now over the "Kauai tracking station," pronouncing it "Cow-Eye."
In the beginning scene, Roy announces a "Meteorite shower." A Meteroite is a chunk of rock from space that strikes the surface of Earth. Roy should have said "Meteor shower."