Revealing mistake: When Homer placed the rocket on his fence and lit it his friend asked "Should we get behind somethin'?" That's when the rocket explodes. When you see them fly back you don't need to slow motion it because you can clearly see the wires attached to their backs.
Continuity mistake: When Homer is walking to Snake Root, he has a rolling pin in his box. You can see the pin change positions in the box.
Continuity mistake: When Homer has just been given the gold medal at the National Science Fair, and he turns around to try to spot Werner Von Braun, several of the people in the crowd jump a lot closer to him when he turns back around.
Continuity mistake: When the miners decide to strike, we hear the sounds of a major storm. As they walk out the door, the rain is coming down heavily. However, in the very next shot, a long shot of the same scene, there is no rain.
Continuity mistake: When they burn down the shack where they lit off rockets, O'Dell is seen to be the last one turning around and in the next scene he turns around again.
Continuity mistake: In the first shot of the train scene there is no turn off track but in the next shot one appears outta nowhere. Hell it's even in a different spot judging by the lack of shrubbery in one of the shots.
Factual error: As Homer and his friends attempt to flag down the train after dislodging the old rail, the engine seen is of the 2-8-2 wheel arrangement with markings of the Norfolk and Western Railway. The Norfolk and Western never owned any 2-8-2 locomotives, preferring instead engines of the 4-8-0 arrangement.
Other mistake: Throughout the film, the Hickams' phone buzzes. When Elsie throws the phone into the yard, it breaks to reveal a pair of bells.
Factual error: This movie takes place in 1957, clear from the Sputnik reference, but at the dance they play "It's All in the Game" which didn't come out until 1959.