Revealing mistake: The majority of the Army rifles and all the machine guns are obvious props, incapable of even firing blanks. If you watch carefully when they're "firing" you can see that the muzzle flash is actually animated and no shell casings are coming out. The sound has been added in post production. This is most obvious when the general is firing a havy machine-gun (with no belt) at the saucer over the capitol. (00:55:05)
Revealing mistake: After the Martian who is dressed up as a women spits a finger in the fish tank a bit of the Martian's mask near its mouth is torn away. As she chews the nitrogen gum the human lips move but her real teeth don't. (01:04:20)
Revealing mistake: When the Nancy Reagan chandelier fall on the first lady, it is obviously a dummy with a wig. (01:10:30)
Revealing mistake: At the end of the film, when the singer holds out his arm and the hawk flies on to it, you can see the pad under his sleeve that would prevent the talons from clawing the actor's arm. (01:40:00)
Revealing mistake: When the two boys are playing the shooting game at home, they run away and drop the guns, yet the fish or whatever they are keep on getting blown up.
Chosen answer: While the movie is a parody of the 50's sci-fi B-movies, the film is actually based on the Topps 1962 science fiction trading card collection called "Mars Attacks!", which tells the tale of the Martians' attack.
Bishop73