Cassandra Truth: Bubbles already suspects that the cat their were trying to keep is the real mastermind, but the others don't believe her until they see him in action while controlling Utonium.
Cats Are Mean: The talking cat is very evil, being able to make any human his partner in crime.
Cat Up a Tree: The cat ends up stuck in a tree. Nobody came to help him because he was the episode's villain.
Cute Is Evil: The cat is very adorable, and even Buttercup loves it. However, it ends up being shown to be the villain of the episode.
The Dog Was the Mastermind: At first, the cat is seen working alongside another man during a robbery, however it is proven at the end that the cat was the one behind the whole heist. His plan is to use a jewel-powered machine that can hypnotize Townsville and the world into serving all cats.
Laser Hallway: The cat hypnotizes the Professor and the two go to the museum to steal the Catseye Jewel. The Professor puts a container of grease on the floor and slides the cat under the lowest beam, leaving a trail of grease behind. The Professor then does the same and they steal the jewel.
Won't Take "Yes" for an Answer: The girls are awaiting the Professor's decision on whether they can keep the cat. The Professor enters the scene and says, "We can keep Kitty!" Bubbles starts bawling instantly and the other two are complaining before they realize he said yes.
Impeach Fuzz contains examples of:
Arson, Murder, and Jaywalking: The girls and Ms. Bellum try to convince The Mayor to take back his rightful position; they tell him that Fuzzy won't let the girls fight crimes, has turned his office into a literal example of a pigsty, is tarnishing the image of what it is to be the Mayor, and is wearing his hat. The last one is the Mayor's Berserk Button.
Go-Go Enslavement: While it isn't "enslavement", Ms. Bellum clearly isn't happy about the outfit she has to wear when Fuzzy Lumpkins takes over as mayor. It is a midriff-bearing and cleavage-exposing Daisy Duke ensemble, and a pair of short-shorts made from cut-off jeans.
Tin-Can Telephone: When Fuzzy is elected mayor, he replaces the Powerpuff Hotline with a tin can.
Villainy-Free Villain: Fuzzy wins the election fair and square, and while he is terrible as mayor, he doesn't actually do anything evil or illegal while in office.
What an Idiot!: The Mayor chooses the Professor to help him fight Fuzzy and his relatives instead of the Powerpuff Girls. Also an In-Universe example, as the Professor calls him out on this stupid decision.