Marshall Richard "Dick" Dix, a special detective, saves a fast food chain restaurant from a terrorist hostage situation, much to the displeasure of the police chief. He drives away, and back to the police station, where he meets his boss, who is with a police worker, Cassandra Menage. She retells her experience of the cloning of the President of the United States of America, Bill Clinton, who remains unnamed throughout the film. Dix is sent to the cloning facility, a moon base called Vegan. Dix causes a mayhem on the way there. He reaches Vegan, and is met by Lt. Bradford Shitzu at the security check. On the way to meet the main suspect in the cloning, Dr. Griffin Pratt, Dix experiences strange happenings throughout the colony involving certain Aliens who live there. During a very strange incident involving an Alien about to explode, Dix meets Capt. Valentino DiPasquale, with whom Dix will share his quarters. Dix and Shitzu get to Dr. Pratt's quarters, and talk to him. Shitzu leaves, and Pratt takes Dix on a tour of his cloning facility.
At a meeting of the Astronomic Club, its president, Professor Barbenfouillis, proposes a trip to the Moon. After addressing some dissent, five other brave astronomers—Nostradamus, Alcofrisbas, Omega, Micromegas, and Parafaragaramus—agree to the plan. They build a space capsule in the shape of a bullet, and a huge cannon to shoot it into space. The astronomers embark and their capsule is fired from the cannon with the help of "marines", most of whom are played by a bevy of young women in sailors' outfits. The Man in the Moon watches the capsule as it approaches, and it hits him in the eye.
In 1965, a series of mysterious and devastating incidents are happening on Earth. These incidents range from a railroad bridge levitated off the ground causing a train wreck in Japan; an ocean liner lifted out of the Panama Canal by a waterspout, destroying it; severe flooding in Venice, Italy; and the destruction of the J-SS3 space station.
Phineas T. Barnum (Burl Ives) and friends finance the first flight to the moon but find the task a little above them. They attempt to blast their rocket into orbit from a massive gun barrel built into the side of a Welsh mountain, but money troubles, spies and saboteurs ensure that the plan is doomed before it starts...
The spaceship AAB Gamma is dispatched from Japan to travel to Mars to investigate reports of UFOs in the area. When the Gamma nears the red planet, it comes across a mysterious alien vessel that sprays the ship with spores. Samples are taken back to earth where one of them begins to develop.
In the British city of "Everytown", businessman John Cabal (Raymond Massey) cannot enjoy Christmas Day, 1940, with the news everywhere of possible war. His guest, Harding (Maurice Braddell), shares his worries, while his other friend, the over-optimistic Pippa Passworthy (Edward Chapman), believes it will not come to pass, but if it does, it will accelerate technological progress. An aerial bombing raid on the city that night results in general mobilisation and then global war.
In the year 1946, the Soviet space program is undergoing turmoil. Professor Sedikh, who is planning to lead the first manned exploration to the moon, is denounced by his rival Professor Karin as being too old and too mentally unstable for the mission. Professor Sedikh, aided by his assistant Marina and a youth named Andryusha, disregard Prof. Karin’s authority and make a successful landing on the moon. Although a few problems occur at the moon, including the discovery of a damaged oxygen tank and Professor Sedikh’s becoming trapped under a fallen boulder, the expedition is a success and the cosmonauts return to Moscow.
Financial disaster looms for Grand Fenwick when the current vintage of its only export, wine, starts exploding in would-be consumers' faces. Prime Minister Mountjoy (Ron Moody) decides to ask the United States for a loan, ostensibly to fund its entry in the race to the Moon, but actually to save the duchy (and install modern plumbing so he can have a hot bath). The devious politician knows that the Americans will not believe him, but will consider the half million dollars he is asking for to be cheap propaganda supporting their hollow call for international co-operation in space. He is delighted when they send him double the amount as an outright gift. The Soviets, not wishing to be one-upped by their Cold War rivals, deliver an obsolete rocket. Mountjoy asks resident scientist Professor Kokintz (David Kosoff) to arrange a small explosion during the "launch" of their lunar rocket to make it look like they have actually spent the money as intended.
The radio telescope at Parkes (Parkes Observatory), New South Wales, Australia, was used by NASA throughout the Apollo program to receive signals in the Southern Hemisphere, along with the NASA Honeysuckle Creek Tracking Station near Canberra.
Two escaped convicts, Gary (Tommy Cook) and Lon (Gary Clarke), are discovered hiding aboard a rocket by scientist Dirk Green (Michael Whalen), who then forces them to pilot the spaceship to the Moon. Dirk, who is secretly a Moon man, wants to return home.
The film begins with footsteps leading to a pond. The camera continually moves upwards to show the flight of butterflies, birds, and a progression of historical aircraft ending with a rocketship travelling through space and landing on the moon.
On July 20, 1969, during the last phase of the Apollo 11 mission to the Moon, a robotic eye emerges from the lunar soil and takes notice of the landing module as it takes off. The eye buries itself again.
As Wallace and Gromit relax at home, wondering where to go on vacation during the upcoming bank holiday, Wallace decides to fix a snack of tea and crackers with cheese. Finding no cheese in the kitchen, he decides that the pair should go to a place known for its cheese. A glance out the window at the night sky gives them the idea to travel to the moon, since, according to Wallace, "everybody knows the moon's made of cheese." They build a rocket in the basement and pack for the trip, but after lighting the fuse, Wallace realizes that he has forgotten to bring any crackers. Hurrying to the kitchen, he grabs several boxes and returns to the rocket just in time for liftoff.