The war was over . . . The only survivors were street animals - dogs, cats and rats. From them, a new race of mutants evolved. That was a long time ago. Mok, a legendary super rocker, has retired to Ohmtown. There his computers work at deciphering an ancient code which would unlock a doorway between this world and another dimension. Obssessed with his dark experiment, Mok himself searches for the last crucial component: a very special voice.
After the End: There's some jazz in the prologue about how an apocalyptic war killed off all the humans and now extremely anthropomorphic animals have taken our place as detailed in the quote above. It has absolutely no bearing on the plot at all, just go with it.
Air-Vent Passageway: Cindy Schlepper escapes this way every Saturday night, apparently, which is convenient for Angel.
By the Lights of Their Eyes: Mok is often shown this way, especially in the first twenty minutes of so of the movie where he's only ever shown in shadow, with only his eyes visible.
Card-Carrying Villain. Mok. ("My name is Mok, thanks a lot. I know you love that thing I've got. You've never seen the likes of me; why, I'm the biggest thing since World War III - girls?")
The Caretaker: Toad seems to be this with his brothers and sister. It doesn't stop him from being a jerk to other people, though.
Cat Girl: Angel may be either this or a rat girl. Singing voice of Debbie Harry no less! (Her speaking voice was Susan Roman.)
Chekhov's Gun: Ohmtown's name sounds like an Incredibly Lame Pun on "Hometown". Then Mok finds he needs more electrical power for his summoning rite, and you realize "ohm" is a good name for a town with a gigantic power plant.
Furry Confusion: The scene where a Dog-Woman character gives a Rat-man a tattoo of a traditional mermaid (fish tail on a human lady) as a non-anthropomorphic cat looks on is practically a Lampshade Hanging.
Funbag Airbag: Stretch turns right and his face wedges into a lady's chest in Club 666. She doesn't appreciate it.
Mok: (completely unfazed): "Thank you. Shall we see them off?"
It's All About Me: Mok, to the point where it often falls squarely into A God Am I territory - this is a man who routinely writes songs solely about how divinely awesome he is, and how everyone must worship him. When people don't completely worship him, he snaps and decides to summon a demon to teach them a lesson.
"I Want" Song: Angel's song qualifies. It's essentially about her faithfulness to Omar, despite his apparent coldness.
Monumental Damage: Played with in a shot of the Statue of Liberty, still standing but tilted and battered, with ramshackle houses attached to her sides. Apparently she survived the war, but is no longer considered anything more than odd-looking real estate.
No Man of Woman Born: Mok's computer predicts that the demon can only be turned back by "the magic of one voice, one heart, one song," but then adds there is "no one" who can stop his plan. Mok doesn't count on Omar and Angel singing one song together, Angel with her mystically-attuned voice and Omar because his heart finally beat out his ego and let him sing something she wrote.
Non-Ironic Clown: Zip's favorite cartoon is "Uncle Mikey", starring a short, pudgy cartoon clown with a big, goofy grin. Though his choppy animation and grotesque face can be off-putting, he's genuinely nice and teaches kids the difference between good and evil.
We don't see anything of what Mok was like when he started his career, he could have been considerably more appealing and his long career having resulted in his ego expanding to the point of his decay into the evil he became. This would explain his ratings dropping to the point he can't sell out his concerts anymore, he simply couldn't conceal his evil enough anymore and only the most blind fans remained.
Panty Shot: There are none of these, as it's easier to describe when you can't see Cindie's underwear.
Take That: The "Uncle Mikey" scene and the conversation between Mok and his minion afterwards, in addition to being one of the best scenes in the movie, is a straight-up slam on moral relativism.
Albeit a very ham-fisted one that really comes across less like a philosophical belief and more like a destructive asshole using the Theme Park Version of moral relativism/subjective morality to weakly justify his desire to destroy others for petty reasons.
He also has a more minor freakout earlier in the movie after another defiant speech by Angel. He goes into his costume room and goes completely beserk for a little while before one of his henchmen find him.