The boys created a remote ignition device by having a spring-loaded match rub past a match strike strip and then light the fuse. The strike strip they used was the modern "polka dot" kind. In 1957 all the strike strips were solid strips.
When Roy Lee's stepfather is beating Roy Lee up, after getting released from the jail, and John Hickam tells Homer to get into the car, Jake Gyllenhaal (Homer Hickam) is not the one getting into the car, it is his body double.
During the last launch sequence where John Hickam launches the "Miss Riley" Homer Hickam activates the launch box by flipping a switch on the box with one hand. In the next shot, it is apparent that he used his other hand to flip the switch.
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.
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).
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.
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.
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.)
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.
In the auditorium scene near the end of the movie, the U.S. flags are hung incorrectly. The blue field or union should always be displayed in the upper left corner no matter if hung vertically or horizontally.
When Homer and Quentin estimate the range of the Auk XIII, it's presumably done with a 50-foot rope, since they measured off 126 rope lengths to get to 6,300 feet. However, in scenes that show the full rope length, the rope is no longer than 30 feet, about five times Jake Gyllenhaal's height of 6 feet.
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.