SpongeBob visits Sandy's Treedome, and then sees that Sandy had built a rocket ship. Sandy explains to him that she is going to the moon, and SpongeBob begs her to take him with her. Although she insists that he cannot come, SpongeBob's begging ultimately convinces her to let him come with her.
That night, Patrick comes to SpongeBob's house and gives him some "Alien Repellent," which they sneak into Sandy's treedome to spray on the windows. Even though they agree to only spray the windows, Patrick inadvertently enters the rocket, and SpongeBob follows. After playing with the ship's various features, SpongeBob accidentally starts up the rocket, which loops over the moon and then comes back to Bikini Bottom. SpongeBob and Patrick convinced that they're now on the Moon, think that the aliens are projecting their memories onto the environment to trick them.
They begin catching everyone with Sandy's net guns (intended for harvesting moon rocks), believing the citizens of Bikini Bottom are aliens. Eventually, after capturing everyone in Bikini Bottom, including Sandy, who attempts to explain the truth to them, SpongeBob is convinced that Patrick is an alien. Patrick attempts to shoot him before he has a chance to capture him but ends up shooting and capturing himself. SpongeBob starts the rocket again to return home, and when it reaches the moon, the rocket crashes on top of it, having run out of gas. Noticing things are different, SpongeBob looks out the window to see the Earth where he realizes his mistake. All the captured fish, who are being stored in the cargo hold of the ship, say: "SpongeBob, we aliens would like a word with you." as the episode ends.
SpongeBob and Patrick in their space suits were designed by Todd White.
There was a deleted scene where Plankton steals a Krabby Patty, but SpongeBob and Patrick capture him. Then Pearl was seen shopping in the mall before SpongeBob captures her. This was likely cut to save time. These scenes can be seen in a book based on this episode. 
This is the third episode in which Sandy Cheeks appears.
When SpongeBob looks out at the window towards the moon, the view of Earth from the Moon looks almost exactly like the famed Apollo 8 photograph.
During a Nickelodeon movie (The Rugrats Movie) promotion in 1999, a set of scratch and sniff stickers were released at specified fast-food restaurants to be used with certain Nicktoons. One of them was used when Patrick squirts toothpaste in SpongeBob's peanut butter. Another one of them was used when SpongeBob pulls out a hot water bottle from Squidward. Also, the symbol that signaled one to "sniff" at the bottom right part of the screen was accidentally filmed along with the episode, and not edited out until late 2002, almost three years after the scratch and sniff packs were put out of circulation.
There is a Lego set called "Rocket Ride (3831)" which is based on this episode. Also, it was also the first Lego set to include Sandy as a minifigure.
A chapter book based on this episode features extended material: In the extended ending, SpongeBob releases Patrick and Sandy from the bags, and Sandy shoots SpongeBob as punishment before flying the rocket back to Bikini Bottom (This ending would be impossible in the actual episode because the rocket ran out of fuel when SpongeBob flew the rocket back up to space a second time which caused it to crash onto the moon, unless Sandy had an extra supply of fuel somewhere aboard the ship.) The book also shows Plankton getting captured while stealing the Krabby Patty formula, and SpongeBob and Patrick capture Pearl, which according to the book, acquired more than one net to do so. These scenes are not in the episode version.
This episode shows that Mr. Krabs has a pet worm. This worm would later be seen in "As Seen on TV."
He also had a pet worm in one of the SpongeBob Comics.
This is the first time that Mr. Krabs is seen only outside of the Krusty Krab during an episode.
This marked the first episode where Mr. Krabs appears without the Krusty Krab appearing.
When Patrick plays on the video game, he makes a face that is now an Internet meme.
Netflix mistook the name for, "Sandy Rocket." However, it was later renamed back to "Sandy's Rocket."
This is the first time SpongeBob and Sandy go to the moon. The second will be in "Mooncation."
This is the first episode that shows that Sandy is interested in science. This would become a more common part of her in post-movie episodes.
This episode possibly takes place after "Suds" (another Season 1 episode) and "Dumped" because Patrick put his toothpaste on SpongeBob's peanut butter.
This episode most likely took place after "Christmas Who?" since SpongeBob wears a Santa hat to bed in this episode, which indicates that Christmas has already been brought to Bikini Bottom.
The sounds heard when Patrick is playing a video game are like the sound effects from the Game Boy version of Tetris.
When SpongeBob and Patrick first become weightless in the rocket, a book floats by with "2001" written on its cover. This is a reference to the novel 2001: A Space Odyssey.
SpongeBob's belief that the "aliens" are projecting his and Patrick's memories of Bikini Bottom onto the lunar surface to put them into a false sense of security seems to be inspired from "The Third Expedition," from The Martian Chronicles. It could also be inspired from the ending to the movie "Contact."
The word alien Sponge Bob had a Selenites.
SpongeBob makes reference to "cowlicks" as evidence of aliens. This is most likely an homage to Pete & Pete, a very early Nickelodeon live action show.
The music heard when SpongeBob launches into space the second time is a parody of the Star Wars theme music.
The scene when SpongeBob and Patrick "analyse" Squidward thinking he's an alien has some references to the 1979 movie, Alien most notably when Squidward's tentacle attaches to Patrick's helmet like the series "Facehuggers' in the famous scene from the film, and the way Spongebob's hands appear under the light in Squidward's water bottle are similar to the way the eggs in Alien appeared.
When the rocket begins to lift off and smoke is created from the launch, Sandy smells it in her bedroom. This is physically impossible as the rocket was outside of the treedome and the dome is airtight with Sandy inside.
Before throwing Sandy in the rocket to bring to the moon, Patrick laughs, but his mouth does not move in the sync with the laugh.
At the start, SpongeBob was about to enter Sandy's Treedome without a water helmet.
When SpongeBob asks Sandy what she is going to do on the moon, SpongeBob says: "Are we gonna hunt aliens on the moon?" However, the closed-captions said, "Will we hunt aliens on the moon?"
When the rocket first circles the moon, the rocket is almost as big as the moon. But at the end of the episode when SpongeBob looks out the window, the moon is much bigger.
SpongeBob and Patrick experience gravity turning on and off when leaving the water. But gravity wouldn't change until they left earth's atmosphere.
When SpongeBob and Patrick are floating in the rocket and Patrick is trying to get right side up, SpongeBob laughs completely out of tune.
The rocket leaves a fire trail behind it, but when it crash lands, it uses a propeller.
When SpongeBob and Patrick are trying to stuff everyone into the ship, it appears to be full. However, they have enough room to throw Sandy in later.
At the beginning, there is a ladder to get onto the platform. Then, in the next scene with the platform; the ladder is gone.
In one scene where Sandy is showing SpongeBob how the net gun works, she blows on the bubbles coming out of the gun, despite having her helmet on.
When the fish holding the parasol is netted, her eyes appear on its canopy. Her eyes should appear underneath the canopy, not on it.
In reality, it would take a few days to arrive at the moon, not a few minutes (or hours). The only probe to do it in less time was the new horizons probe headed for Pluto (about 6 hours) and it only passed the moon's orbit around the earth, the moon itself was not close enough to give it a "lunar slingshot."
If the rocket ran out of fuel, it's unknown how everyone was able to return to Bikini Bottom.
Patrick and SpongeBob should have figured out Sandy wasn't an alien since she was landing from the sky. They should have figured out that it was the real Sandy, following them to the moon.
In this episode, SpongeBob's alarm clock is on the left side on the bed, unlike in most other episodes.
When SpongeBob says: "a present" his speech is cut off so it sounds like a prese-.
When Sandy jetpacks up to the Moon and lands, she takes up almost the whole top surface of the moon, which is a size error.
When SpongeBob and Patrick see Mr. Krabs, he is with his pet worm Mr. Doodles. When they capture Mr. Krabs and throw him in the rocket, Mr. Doodles is absent, and not captured.
When SpongeBob launches the rocket the 2nd time and lands on the moon, it is unknown how he could have done this because after crash landing in Bikini Bottom the rocket was almost completely lodged into the ground.
Before Squidward wakes up, SpongeBob is holding on to three of his tentacles, the fourth one is still in bed. However, in the next close-up of Squidward, SpongeBob is holding on to all four of them.