This episode contains examples of the following tropes:
Adults Are Useless: The Muddlefoot parents and Drake Mallard completely ignore Honker's warnings about the spaceship crashing from the sky. It's up to the two children, Honker and Gosalyn, to stop the alien invaders.
Artistic License Biology: Nikto, being a Big Eater, is happy to take over the body of a cow with four stomachs. When Flarg forces him to switch to a sheep's body, he complains that now he has only one stomach. Sheep are ruminants with four stomachs just like cows.
Big Eater: Nikto is a Brainteaser with a huge appetite. Honker takes advantage of this in the climax, throwing him a metal can full of pepper.
Cassandra Truth: Nobody but Gosalyn believes Honker when he tells them that he saw a fire ball falling from the sky, and later they don't believe them when they tell them about the Brainteasers.
O.O.C. Is Serious Business: Launchpad initially doesn't believe Gosalyn that hats have taken over Drake and Honker's bodies. He spots them, with the hats on their heads and talking in different voices, and doesn't see anything odd... Until Drake transforms into Darkwing. "You're right, DW would never wear a hat that clashes with his outfit."
Planet of Hats: The Brainteasers are the most literal example of this trope, being actual sentient alien hats who hop onto other beings' heads to control them.
Puppeteer Parasite: The Brainteasers are able to control people after latching onto their heads.
Take Over the World: Flarg was initially interested in leaving the Earth. When he found out this planet has nuclear missiles, he decided to take over the world and add it to his empire.
Weaksauce Weakness: Pepper and dust easily causes the Brainteasers to sneeze, which in turn will force them to lose control of their hosts.