Junior Tracy does a police artist sketch of a hold up suspect who murdered the husband of Mrs. Koob during a hold up while his wife, Moon Maid writes jokes for the Sawdust comic strip at $20 a piece. On her way home from the Sawdust studio she is held up by the same two crooks, named Burly and Jez. She zaps them with her energy powers and after judging they will survive goes home, worried the power use might jeopardize her stay on Earth. The two burnt hoodlums are seen by a bus driver and soon matched to Junior’s sketch.
Burly and Jez work for a man named Matty Square, a small time boss and cigar smoking cat owner who vows to handle this Moon Maid after what she did to two of his men. Wearing a cummerbund rigged with four pistols, he approaches Moon Maid on her walk home in the park but is zapped and temporarily paralyzed for her troubles. Meanwhile, police have begun to look into the vigilante who took down the two flash fried hoodlums in the hospital.
When a woman on the street is attacked with a knife during a purse snatching, Moon Maid again lashes out, zapping the slasher and then quickly leaving the scene of the crime. The Press picks up on the second vigilante incident and begins calling the unknown individual the “flamethrower”. Trying to find a way around her powers, Matty orders his best wheel man, Hub to run her down in a hit and run. Hub misses and kills a different woman instead before Moon Maid incapacitates him with a zap to the head. Hub is hospitalized and arrested and Tracy begins to narrow down the possibility that his daughter in law is the vigilante. Still, he and Chief Patton don’t want to make a move, feeling she has done nothing wrong and knowing she had promised not to use her lunar blasts on threat of expulsion from Earth.
Matty has become frustrated and obsessed with winning his fight with Moon Maid and orders two more of his men, Crease and Buster to lay a trap with a 220 volt electrified net they intend to drop on her during the walk. All goes well and the net drops on their target, but the plan backfires when Matty connects the wrong wire and both of his men are electrocuted instead. This time the assailing hoods are killed and Moon Maid is upset with the frequency of the attacks. She is going to have a baby and wants to return to the safety of the Moon but after conferring with Junior decides to stay on Earth for the birth.
With only one man, Cokey, left on his roster, Matty deplores the loss of his men and considers hiring new men, such as Fleaface Benny and Blood Carson to help with his next revenge scheme. Square rents a vacant bank and turns it into a false store with the bank vault as a freezer. He then calls Moon Maid to inform her she has won 200 free frozen TV dinners if she wants to come down and retrieve them. Moon Maid is overjoyed, because frozen TV dinners are the only thing she can cook.
Moon Maid falls for the trap and is locked in a vault. Matty and Cokey cackle, intending to leave her there for the next eight months, during which time she will surely starve to death. Their captive has other powers at her disposal though and she uses her telepathy to contact her father for help. The Governor of the Moon has been making a bi-weekly trip to Earth to trade carbon crystals for titanium with Diet Smith. He hears her call and rescues her but forces her to return to the Moon with him. Meanwhile, Junior and the police search for a missing Moon Maid and find the bank with the body of Cokey, an empty vault and reports of a flying cylinder. Matty Square, defeated once again sits alone in his office, with only his cat for company.
When the Governor of the Moon rescued Moon Maid from Matty Square’s vault he immediately took her back home to Moon Valley despite her pleas to be reunited with husband Junior. Junior, Dick Tracy and the detective team surmise that Moon Maid was taken home by her father and Dick and Diet Smith having a sit down meeting on Earth with the Governor to convince him to let Moon Maid return. Junior has a different plan. He creates a paper machine helmet with horns that gives him the silhouette of a Moon man, disables his father in law’s Space Coupe by removing its Atomic Amplifier and then taking Diet’s personal Space Coupe back to rescue his wife.
Junior’s ploy initially works and he reaches the penthouse holding Moon Maid and the pair are reunited. The Governor is furious and after tense words with Diet and repairing his Coupe he quickly flies back to Moon Valley with violence in his heart. He blows up Junior’s Space Coupe, preventing the pair’s escape. He then personally approaches and threatens Junior but the Governor’s wife steps in to calm him and inform him that he is going to be a grandfather. The Governor is overjoyed by this news and agrees the couple should remain together, providing they both agree to stay on the Moon forever. Junior and Moon Maid reluctantly agree and write a letter informing Tracy of the new arrangement.
Following their Moon focus, the detectives get back to their hunt for Matty Square who has hired “Bulldog” Kerson to kill Dick Tracy. It seems his desire to do in Moon Maid has now transferred over to father in law, Dick Tracy. Kerson baits the detectives into following him while he makes a call to Matty Square and then turns and takes a shot that narrowly kills the ducking Tracy. The detective returns fire twice, mortally wounding Kerson who reveals he was hired by Matty Square before he died. The detectives, having recorded the number Bulldog dialed have Square’s address and raid his hideout but Matty escapes ahead of time.
The genial yet eccentric Mr. Bribery and his secretary Miss Deal visited by Matty Square seeking help from a bigger fish. Bribery is extremely kind to Square, offering him all kinds of hospitalities while pick-pocketing everything of value when Matty is not paying attention and goes so far as to gift him money from his own wallet. Bribery shows off his collection of shrunken heads, those who have wronged him in the past, such as Soapy Lava.
Mr. Bribery agrees to hire on Matty Square, although he forces Square to give up his cigar smoking cat. Tracy, who has found the cat’s pedigree in Matty’s old office uses this clue to locate Square and place a video camera in his car. Matty tools to various stops including one to Nah Tay, a South American rug weaver who also moves cocaine. Square then returns to Bribery who elaborates that Nah Tay has a special set of skills, including shrinking heads for Mr. Bribery.
Lizz goes undercover to Nah Tay’s shop and returns with a drug sample she picked up with a piece of tape. Nah Tay though is suspicious and reports back to Bribery and determine Lizz was a policewoman. Nah Tay immediately moves out of his store ahead of a police raid, leaving behind a serious looking cooking cauldron. Bribery has Nah Tay pick up Matty Square and while returning they find the police video camera in his car. Things look dire for Matty and Nah Tay is very upset. Mr. Bribery forces Matty to take a lie detector test to prove he was not working with the police. Matty passes.
Back at the station the detectives watch the first broadcast of the Moon’s new television channel, ran by Junior Tracy from the Moon but a break down in communications leaves Tracy hanging about the possible birth of Moon Maid’s baby. The communication issue was caused by an antenna failure and the Moon Governor returns to Earth in the Space Coupe for parts. He grudgingly agrees to take Junior and Moon Maid along for the flight. Half way between the Earth and the Moon, the baby is born and we see little Ho. Little Honeymoon Tracy returns to Moon Valley and is introduced to her Earth family over the airwaves and soon after Grandpa Tracy visits the Moon for a celebration.
On Earth, Matty Square passes his polygraph test and is put back to work by Mr. Bribery, this time with his long-haired sister, Ugly Christine. Ugly Christine brands Square with a “B” on his forehead, like has been done to all of Bribery’s best employees. His new mission, much to Matty’s dismay, is to kill Dick Tracy.
While Matty is given the heavy lifting, the plan to kill Tracy is devised by Mr. Bribery. They switch on the police video camera and give enough evidence to lure Tracy to a meat-packing plant that was to be Nah Tay’s new base of operations. There Matty is made to hide himself in a barrel with a tommy gun, lying in wait until Tracy arrives. A trapdoor is also installed that drops a victim down into a bubbling vat of boiling water. Matty is only required to fire on Tracy if he fails to be killed by the trap. Bribery and Christine set the trap and Matty hides away in his barrel, but Mr. Bribery, not much for field work, bumps the barrels on his way out and Square rolls down into the vat of water. With a pained scream Matty Square is killed.
The police find Matty Square’s body and close the case on him, but are aware that Nah Tay and someone else was involved in a plan to kill them. Mr. Bribery is saddened to lose his latest employee but consoles himself in private conference with his favorite rose and takes ownership of Matty’s cat, Kitty, whom he forces to smoke cheaper cigars.
While the Tracy and their Moon relatives celebrate Thanksgiving together on Earth, Mr. Bribery hatches another plan to kill Dick Tracy. Nah Tay, who is revealing his shamanistic witch doctor side more and more refuses to cause harm to anyone from the Moon, holding the Moon Gods sacred. Bribery moves forward without involving Nah Tay and his sister Ugly Christine poses as a photographer wanting to take pictures of Junior, Moon Maid and Honeymoon in the snow of an observatory. Christine’s inability to operate a camera betrays her true motives though and Mr. Bribery leaps out of nowhere, attempting to gas Junior. Bribery, once again a failure in the field, forgets to pull the pin and is pushed away after which Moon Maid zaps the pair.
Junior and Moon Maid take Honeymoon back home to safety and though they try to keep it a secret at first eventually tell Tracy and the Moon Governor about the attack. Luckily for the two criminal siblings, Nah Tay shows up takes their frozen bodies out of the snow and revives them with the help of a Doctor A. M. Dawn at his home. Sam Catchem is staked out at Nah Tay’s home from a nearby building and although he did not see Bribery or Christine arrive, he does see the doctor visit. Nah Tay sees Sam as well, and attacks him from behind, taking Catchem’s hat off with a deadly knife throw. The two wrestle before Nah Tay leaps from the three-story rooftop and lands unharmed, escaping into the night.
During the fight, Mr. Bribery’s secretary Miss Deal arrives and helps him and his sister escape back to his office. Initially he fears Nah Tay was arrested but instead the South American arrives with a knife wound on his arm. Mr. Bribery finally asks that Nah Tay handle Dick Tracy and the witch doctor spends a week taking drugs and expanding his mind for the mission. This entire episode is captured on camera by Bribery so when Nah Tay decides to switch sides and kill Bribery instead, the boss acts.Diet Smith’s second space coupe pilot, a man named Maay is paid a handsome $5,000 to assist two of Mr. Bribery’s thugs who pick up Nah Tay with Smith’s newest space coupe and jettison the head shrinker into orbit.