T.D. is visiting the Lorraines, and he and Helen are eating yogurt, but Martha is sulky that she's not allowed any. She claims that this, along with being barred from Helen's school, are examples of dogs being "discriminated" against. T.D. tries to cheer Martha up by giving her the comic he wrote in the previous episode about the planet of dogs. After reading the comic, she falls asleep and dreams that she's one of the dogs on the planet.
The dream begins with Martha waking up on the planet and giving a lecture to a pack of her lookalikes about the universe. She mentions that Earth has only one moon, upon which the Chuck Nebula comic was left, but she thinks Chuck Nebula was a real person. She notes that nobody knows Chuck's fate due to the comic ending on a cliffhanger, so her superior (also named Martha, as are all of the dogs apparently) assigns her to fly to Earth to find out.
She flies to Earth, but (obviously) can't find Chuck Nebula. She does, however, see a man stealing a dog, so she decides to interfere. After being seen by a crowd, including the Parkingtons, she finds him going into the pet store with the dog tied to a bollard outside, then sets the dog free but is caught by the man. He chases them into a dead end, but Martha digs herself and the other dog to safety.
They end up near a restaurant, enter, and try to order only to be kicked out. Martha is indignant at Earth's legal system, then she sees a piano attached to a fraying rope while a woman is approaching with a baby. The piano falls and Martha grabs it just before it lands on the baby, then puts it on the roof.
Meanwhile, Mrs. Parkington and some others are talking to the mayor about the "alien invasion". The mayor leaves, then Martha finds out that the other dog has never heard of Chuck Nebula. The man who tried to steal the other dog distracts a hot dog vendor by pretending there is a parade, then steals his cart. Martha uses her telekinesis to bring the cart back to the vendor and lift up the thief. She berates him for being unethical (while revealing that the other dog's name is Davey) and scares him away.
Just then, however, the waiter points Martha and Davey out to Kazuo, and Kazuo locks the two dogs in the pound. Martha opens the other dogs' cages with her telekinesis (while learning that Earth dogs don't have it). She then gets hungry and raids the pound owners' fridge, with the other dogs sharing the food.
The Mayor's office offers a reward for whoever stops the alien invasion, intriguing the thief since he's greedy. The dogs walk past, with Martha explaining that she's an alien, then the thief jumps out. He claims he's turned over a new leaf and wants to invite Martha to a "Welcome to Earth" party at the Mayor's office.
The Mayor herself arrives, and when the thief explains that Martha's the alien, the Mayor tells a police officer to arrest her while she leaves for another town. However, Martha picks up the Mayor's truck and demands to know why she should be locked up. The Mayor says that it's in case Martha is dangerous, but Martha says she comes in peace and would like to talk to Chuck Nebula about improving Earth. The thief, worried that Martha would land him in trouble, points at her and pretends she has the Mayor "trapped". Martha, who's just found out that Chuck Nebula isn't real, gets cornered by citizens.
Then, she wakes up and is disappointed to find that she's not actually telekinetic, but happy when Helen feeds her a "cheese snoodle".
This episode provides examples of
- Alien Invasion: Discussed when Mrs. Parkington sees Martha land in her spaceship and thinks that she and other alien dogs want to conquer Earth.
- Aliens Are Bastards: Discussed. While Martha comes in peace, everyone automatically assumes she must be an invader because she's an alien.
- And You Thought It Was Real: In Martha's dream, she sees the Chuck Nebula comic and walks away thinking he was a real person.
- Bait-and-Switch: Martha says she knows what to make with bread, pickles, baloney, mustard, and ketchup... but it's not a sandwich; it's a "delicious mess".
- Bald of Evil: The man who tries to steal Davey is bald.
- Barefoot Cartoon Animal: In Martha's dream, she and the others wear onesies without shoes.
- Big, Stupid Doodoo-Head: Martha calls the dog thief an "inhumane meanie-pants".
- Civilised Animal: Like in the previous episode, the alien dogs can talk and they wear clothes and have a society, but they also walk on all fours.
- Continuity Nod: Martha says she wanted to see T.D.'s presentation about the planet of dogs, which he wrote in the previous episode "Dogs in Space". T.D. then gives her the comic he wrote in said episode to cheer her up, and on her dream, the Chuck Nebula comic is mentioned again.
- Distressed Dude: Davey gets dog-napped by a thief and rescued by Martha.
- Dream Episode: The majority of the episode takes place in Martha's dream.
- Dream People: Martha dreams up a brown dog named Davey, who she saves from a dog-napper, and also dreams up said dog-napper.
- Cyclops: The illustration of the one-eyed alien in the Chuck Nebula book appears again.
- Fantastic Racism: In Martha's dream, everyone thinks that aliens are all bad news.
- Greed: In Martha's dream, the bad man steals pets and a hot dog cart to make money.
- Happy Dance: Martha leaps around happily when she "wakes up" on the planet.
- Heel–Face Turn: Discussed when the thief lies that he's changed his ways to try to get Martha to follow him.
- Heroic Dog: In Martha's dream, she uses her telekinesis to stop a piano from falling onto a baby.
- His Name Really Is "Barkeep": In Martha's dream, the mayor is apparently named Mayor, since when the thief mentions her by her title, she says, "Did somebody say my name?".
- Interspecies Romance: One of Martha's dream lookalikes finds Chuck Nebula (a human) "dreamy".
- I Thought Everyone Could Do That: Martha is surprised that the Earth dogs aren't telekinetic.
- Meaningful Name: This is the second episode to mention the fictional astronaut named Chuck Nebula.
- Mind over Matter: In Martha's dream, she can send beams from her ears with which to pick things up without touching them.
- Nightmare Sequence: Downplayed for Martha's dream. It's mostly a fun dream, albeit a bit frustrating at times, but then turns into a nightmare at the end when the crowd of humans wants to apprehend Martha.
- No Animals Allowed:
- Martha complains about the "mean janitor" never letting her into Helen's school.
- In her dream, Martha and Davey try to dine at a restaurant, only to be kicked out because the restaurant doesn't allow dogs.
- No Ending: The Chuck Nebula comic that ends on an unresolved cliffhanger is mentioned again.
- One-Steve Limit: Inverted in Martha's dream, in which her doppelgangers all share her name.
- "The Reason You Suck" Speech: Martha chews out a criminal for trying to steal Davey and a hot dog cart:Martha: "I'll tell you what's happening: you are getting a lesson in manners! First, you were not humane to Davey here, and then you tried to steal that weenie cart! Now, stop it and get outta here! And be more honest! Like dogs!"
- Shout-Out: Martha's last thing she says in her dream is "There's no place like space", which references the line "There's no place like home" from The Wizard of Oz.
- Stellar Name: Chuck's last name is Nebula, which is a kind of space phenomenon.
- Stock Animal Diet: Martha's spaceship in her dream is bone-shaped and she orders two rare steaks at the restaurant for her and another dog (Davey).
- Talking in Your Sleep: Martha says, "There's no place like space" three times in her sleep before waking up.
- You Are Fat: Helen says that if Martha keeps eating her snacks, there'll be "too much" of her.
