Continuity mistake: The first time we see Tom Jones' backup dancers, they are about three feet apart. In the next shot, they are directly next to each other. (01:12:40)
Continuity mistake: When Byron, Barbara and the others are going to escape from the casino, the Martians break a wall behind them. The hole is different in the following shots. (01:14:40)
Other mistake: In the scene where the President dies, after the General tells everyone to hush and there are agents/bodyguards slowly approaching the door, watch the door to the room before and while it explodes. There are lines in the door which mark the way in which the door will be blown open. (01:25:30)
Continuity mistake: Right before the president is killed, the Martians shoot around in the room and knock over Australia, leaving the lighted outline visible. When Mitch the bodyguard is killed, the cutout is back, intact. When the president starts his speech ("Why are you doing this?"), we see the lighted outline and the cutout is missing yet again. (01:27:15)
Continuity mistake: When the two boys finds the dead Martian in their bedroom at the end of the film, there's that green stuff on his brain but in the next shot, when they push the Martian and he falls into the street, the brain is clean. (01:39:10)
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.
Other mistake: In the scene where they are at the church, the church looks tiny when compared to the car outside. When the camera shows inside the church it's much bigger.
Factual error: When the President holds the meeting in the room where all the countries are on the back wall in blue, Australia is not only the wrong shape (too long) but the wrong way around (the rounded part should be on the other side)
Continuity mistake: When we first meet Lands in the casino, Art sticks a cigarette in his mouth. But in the next shot when he hands Barbara some chips the cigarette disappears.
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