To make the Martian Girl costume as smooth as possible, it had no zippers or buttons on it. Lisa Marie had to be sewn into it every day before filming of her scenes in it could even begin.
Jack Nicholson accepted his role in the film without reading its script, since he had enjoyed working with Tim Burton on the film Batman (1989) and wanted to work with him again.
The film's writers were not sure what the Martians should sound like, so its script used "Ack! Ack! Ack! Ack! Ack! Ack!" for all of their lines of dialogue. This became their actual language in all future "Mars Attacks" merchandise and media.
The design of the Martians' spaceships in the film was inspired by the film Earth vs. the Flying Saucers (1956), including the weapon that looked like a radio dish emanating from the bellies of the spaceships. In both films, it was used to destroy both buildings and people.
When humans were disintegrated by the Martians' ray guns, the resulting skeletons were colored either red or green. Producer/director Tim Burton explained this had been done because the film had been scheduled for a Christmas release. Also, the red and green skeletons were first seen in the film Beetlejuice (1988). When Barbara and Adam were in Juno's office, you can see them with other ghouls looking at the screen.
Tim Burton: [distorted female faces] Nathalie's head is incongruously grafted onto her pet Chihuahua's body by the Martians, the Martian Girl's mask is partially ripped off to show something like a Glasgow smile, and numerous women are disintegrated into colorful skeletons by the Martians' ray guns.