At the end of the movie when they show the space shuttle launch, the first shot shows a launch stack with a white painted external tank. The second shot shows a later, unpainted rust colored tank.
After getting in a fight with O'Dell, Homer walks alone towards Snakeroot with nothing in his hands. In the next shot he is holding a bunch of boxes.
When Homer is writing equations on the chalkboard, explaining to Mr. Turner that they did not start the forest fire, the previous writing on the board gets erased without Homer actually doing so (the sound effects of him writing never stop long enough to erase anything).
After Homer and O'Dell have their fight in the woods, Homer heads out toward the road from the boys. As he passes the car that Roy Lee had just shot up, the headlights are intact again and there are no bullet holes visible in the windshield as before.
The beginning of the movie is dated October 4, 1957. The very next day Homer goes to football tryouts. High school teams played just nine games back then with the first game being the first week of September. Therefore, the team would be about 4 games into the season and would not have open tryouts at the half season mark.
When Quentin first looks at Homer's calculations for the lost rocket, the sheet already has the equation with all the necessary data to calculate the range written down. About 2/3 down the page, the horizontal range formula appears as d = (v² / g) × sin 2A = (450)² / 32 = 202,500 / 32. Solving this gives 6,328 feet, the answer that Quentin writes down later. (This assumes a launch angle A of 45°, which maximizes the range, so that sin 2A = 1.)
The end of the movie states that Homer's father died of black lung disease in 1976. Homer's father actually died in 1989.
In real life, both the father and son were named Homer Hickam, however in the film the father's name is changed to John. This was most likely done to avoid confusing viewers by having two characters with the same name.
During the end "where are they now" montage it says that Freida Riley died of Hodgkin's Disease at age 31. She was actually 32 when she died.
When Homer writes his letter to Wernher Von Braun, he incorrectly sends his condolences for Von Braun's failed attempt to launch the Vanguard Rocket. In actuality, the Vanguard project was spearheaded by the Navy, much to Von Braun's disliking. Von Braun's rocket was a Redstone 2 and was the first American Rocket to reach orbit.
When Homer's dad introduces the football recruiter, he refers to him as from the University of West Virginia. That is incorrect, the school is West Virginia University. John (Homer's dad) does not have a formal education and knows little of colleges/universities, so him making this mistake is not out of character.
When the workers are talking about forming a union, one extra is mouthing the lines of the character speaking as the camera zooms in.
At around 00:37:27, you can see Roy Lee's actor silently voicing out O'Dell's lines regarding the use of gasoline in their rocket, but quickly catches himself realizing that he's anticipating the lines.
During the launch of the last rocket, the closeup of John Hickam's hands holding the ignition box show there are no wires connected to the front of it.
When the phonograph record is changed during the dance at the Dugout, the records are 45 rpm, but the turntables are rotating at 78 rpm.
The boys say they can't weld, yet the fins are welded to the fuselage.
When Homer and his friends are removing tracks from what they believe are abandoned railroad tracks, a train is heard coming down the line. As the boys run to warn the oncoming train, at the last possible moment, the train diverts onto a spur off of the debilitated track. In a similar scene just previous, no such spur exists.
During the montage of the exploding rocket launches, the last rocket goes up, comes back down, and heads for the block house where the boys are standing. Two of the boys run over a dirt mound and take cover on the other side. You can see the small explosive charge that has been blended in to look like a rock (it's white). This goes off a second later when the rocket hits to simulate another failed rocket test.
The miners' union hall has a 50-star flag, but the strike takes place in 1958, a year before Alaska and Hawaii were admitted as states.
Homer is watching a black and white TV which has a wide aspect ratio. Wide aspect ratio TV wasn't available until several decades later. B+W TVs were all 4:3 aspect.
The miners' union hall has a 50-star flag, but the strike takes place in 1958 (a year before Alaska and Hawaii were admitted as states) when American flags had only 48 stars.
The lenses of the character's eyeglasses have Anti Reflective Coating (ARC) which wasn't available for general use in the 1950s.
Homer approaches Quentin in the library within a few months of the launch of Sputnik (October 1957), but the song "Yakety-Yak" (playing in the background during that scene) was released in April 1958.
The shop phone is buzzing, but when Homer's mother throws it out on the ground, brass bells can be seen inside.
In the shot where Homer first steps off the truck after returning from the Science Fair, a camera is clearly visible at the left hand side of the screen.
When Mr. Turner and the boys get into Mr. Turner's station wagon after they have discovered that an aeronautical flare caused the fire, there is a square block or stone (that nearly matches the curb) placed behind the car's right rear wheel, presumably to prevent the car from rolling backwards on the incline and make it easier for the actor/driver to get the car moving forward.