All There in the Manual: Exactly how did Godzilla & Godzooky first meet the Calico and its crew, anyway? Only the original production notes for the show ever divulged that information: because the Calico saved Godzooky from being entangled in some seaweed.
Atlantis: Actually hidden from the rest of the world in a manner similar to Brigadoon.
Attack of the 50-Foot Whatever: Godzilla himself, natch, as well as most of the creatures he was pitted against. Godzooky probably also counts, as he's so big his head is larger than most doorways and he tends to tower over his human companions. It's revealed in the episode The Firebird that the main reason the Calico rarely uses what appears to be a set of optional hydrofoils to reach fairly impressive speeds is because he's so damn heavy he puts a lot of strain on the ship.
Belly of the Whale: Carl, Brock, and the ship get eaten by the Magnetic Monster.
The Captain: Capt. Carl Majors, although he really shares the leader position with Quinn
Continuity Nod: The penultimate episode "Island of Doom" plays the closest to the original Godzilla film, as Godzilla is attacked by the island's defense forces and has to rampage his way across to save the Calico's crew.
Convection Schmonvection: Episode one. The team brazenly walks right into the lava tubes of a recently-erupted volcano.
Expy: Godzooky resembled Minya from the actual Godzilla movies and has often been confused for the same character by casual viewers.
The giant turtle monster in the arctic appears to have been a shout out to Gamera's origin.
Ditto for the volcanic Fire Bird as a stand-in for Rodan.
And the Calico and her crew are obviously based on Jacques Cousteau and his ship the Calypso.
Energy Absorption: The energy beast fed on power from a hydroelectric dam to grow bigger and stronger. Also, in a different episode, a turtle fed on on magnetic fields in order to increase in size and power.
For Science!: Captain Majors sometimes chides Dr. Darien for letting her curiosity lead her into danger. However, her scientific skills end up saving the day more often than not.
Giant Flyer: The Fire Bird, as well as several giant insects.
Heroic Sacrifice: Carl and Brock (who, with the ship, have been swallowed whole, along with a lot of other random objects) are prepared to sacrifice themselves to save the world from the Magnetic Monster. They make it through okay, though.
Human Popsicle: The frozen German submarine. Interestingly, since these Germans are from the First World War (and therefore not Nazis), they turn out to be perfectly decent folks once finally they realize they're in the future and the war is long over. Then a giant squid attacks!
The Kid with the Remote Control: Though the real signal device belonged to Captain Majors, Godzooky (Pete's pet super-lizard) could substitute when required.
Reality Warper: The Dream Stone, although it really only gets used to bring the Golden Guardians to life. It gets smashed before we learn if it could do anything else.
Small Annoying Creature: Godzooky; somewhat subverted, as Godzooky was a good 30 feet tall if he was an inch.
And, even though he's sweet-natured, Zooky is sometimes useful for intimidating human enemies since, you know, he's a thirty-foot tall flying dinosaur.