The beers that Captain Awesome places on Chuck's diploma change position between them being placed and Chuck walking outside to meet Sarah.
The VCR in the home theater room is a black Symphonic with no Hi-Fi. In the close-up shot of Jeff loading the tape, it turns into a silver Sony with Hi-Fi.
Chuck reaches the code screen after scoring 2 million points. In the end scene, when Jeff starts a game the high score is 161550.
ICBMs are ground attack weapons, not anti-satellite weapons.
The Strategic Air Command ceased to exist in 1992 when it was merged into the Air Combat Command. ICBMs, which did fall under its jurisdiction, are now controlled by Air Force Space Command.
Atari is headquartered in New York City, not Los Angeles.
Missile Command was released in July 1980 and "Tom Sawyer" by Rush wasn't recorded until October-November 1980, so it would be impossible for the game to follow the same pattern as the song as was intended, "the mathematical pattern underlying the game is the same."
Video game kill screens are a result of specific flaws in the game's code. As such, anyone with access to a machine, and therefore the program code, could determine exactly what the kill screen would look like without having to play the game to completion.