A.I. Is a Crapshoot: Axe Cop creates "cyborg" versions of himself and Sockarang, and which almost immediately take up vandalism, bank robbing and infanticide. Somewhat justified as their original directive was "watch Unibaby and punch her if she cries."
Abnormal Ammo: The Magic Police's hats turn into bazookas that shoot incendiary rabbits; the poop cannon might also apply, although it's never specified whether poop is the actual payload or just the primer. Bad Santa has a rifle that fires candy canes.
Adam and Eve Plot: Axe Cop's old friend Super Axe and his wife Tracy became the first living things after Axe Cop and Super Axe killed every animal at the beginning of time. They even have a religion devoted to them.
Awesome, but Impractical: Axe Cop communicates with Flute Cop via an invisible walkie-talkie, which serves no real purpose and would be a nightmare to find if dropped. But it looks cool. Or... Doesn't, as the case may be.
Bad Santa: He gets a much larger role this time around (he's responsible for making Axe Cop an orphan) and a totally different characterization (see Deep South, below). He lives on the "South Pole planet" and enslaves or outright murders good children.
Baleful Polymorph: Book Cop sprinkles Fife Cop with eagle blood, turning him into Fife Eagle Cop.
Flute Cop in "No More Bad Guys". First he gets dinosaur blood on him, transforming into "Dinosaur Soldier". Then he eats an avocado and becomes "Avocado Soldier". Finally he asks Axe Cop to wish him back to being Flute Cop, only for Axe Cop to wish for him to become "a giant gorilla with robo-gun fists and a red bow-tie". Flute Cop's wife isn't pleased.
Busman's Holiday: Seemingly inverted in "Birthday Month" when Axe Cop takes Flute Cop on an "important mission" that's actually just a trip to the beach, then played straight when the mermaids appear and then tragically subverted when it turns out to all be a misunderstanding.
Chekhov's Gun: Axe Cop doesn't want Unibaby pooping until his evil cyborg doppelganger needs stopping
Composite Character: Ray from "Taxi Cop" is a mix of comic characters Officer Lightning, Sergeant McQueen, and Telescope Gun Cop. He's also seen playing with an action figure version of Telescope Gun Cop as a child in flashback.
Couch Gag: The opening sequence is based on the first few panels of the original webcomic. The crime that Flute Cop was recruited to stop changes with each episode.
Creator Cameo: Ethan Nicolle confirms here that he had two, as Chubby Doll and a disgruntled merman.
Also the boy looking out the window while Malachai Nicolle provides the opening narration bears a suspicious resemblance to Malachai's previous appearance in the comics...
When Axe Cop meets up with Super Axe again, we learn that he has given up crime-fighting to focus on his marriage.
Hates Being Touched: looks like the show is making Axe Cop out to be this; after he saves some child slaves from Bad Santa, they rush forward to hug him and he stops them with "Not a chance." See also Running Gag.
I Just Want to Be Normal: In "No More Bad Guys", Flute Cop finally undergoes his trademark transformations from the beginning of the comic. By the end of the episode, the bad guy is defeated with the help of Uni-Baby's horn. Flutey (as Avocado Soldier) asks Axe Cop to wish him back to normal (so as to not disrupt his marriage), but Axe Cop instead transforms him into a gorilla with robo-gun fists and a red bowtie.
Kinda Busy Here: During deadly combat with evil cyborgs, Axe Cop answers a phone call from Flute Cop with "What is it, Flute Cop? I'm babysitting."
London England Syndrome: Parodied; "London, England" seems to stand for the whole England or Great Britain in the second episode, and later on, the phrase still comes up, although just "England" also exists.
Magical Society: Magic World, complete with Magic Police, although it's not clear whether Magic World is an actual place or just Axe Cop's fantasy brought to life by Unibaby's horn
Magical Incantation: "Babysitting Unibaby" lovingly preserves the nonsense "magic words" Malachai invented for the comic, although in this version they might just be gibberish Axe Cop concocted to mess with the people of Magic World, since Unibaby's horn requires no magic words. "Abra-ca-handcuffs" is a straight example.
Male Gaze: a first for the franchise; Flute Cop (and the viewers) get a good look at some bikini-clad women in "Birthday Month"
Mr. Fanservice: In the same scene, Axe Cop shows off his perfectly-toned body in a Speedo!
Man Child: It's justified, in that Axe Cop's creator is a literal child, but the show emphasizes this even more. So far, Axe Cop has: pounded on his partner's door in the middle of the night to demand food (to go), decapitated a helpless alien for not liking soda, and declared that everyone must celebrate his birthday for an entire month.
Misapplied Phlebotinum / Mundane Wish: Axe Cop and Sockarang obtain a magic item that can do virtually anything. They use it to go to Magic World... and then fuck with some spectators and give themselves a bunch of money, which they end up not even using.
Mood Dissonance: Axe Cop has just learned who killed his parents. The music is very dramatic. But Sockarang and Flute Cop are just enthused they got Axe Cop a birthday gift he likes.
Axe Cop is never without his cop hat, even when going swimming.
When he obtains the Power of Christmas, it gets transformed into a kickass trapper hat.
As a child he had a red baseball cap with the letter M on it, a gift from his parents due to his resemblance to Mario.
Grey Diamond wears a tall diamond hat (his child fans wear inflatable versions). When he lost everything in Vegas he temporarily replaced it with a traffic cone. During his army days he wore a shorter version with a brim.
Police Are Useless: Axe Cop points out that "The Magic Police are the slowest police." They do seem to be mostly out of shape and not very competent.
The Regular Police are ineffective, having essentially been replaced by Axe Cop.
Pragmatic Adaptation: Certain elements of the original comic have been combined or altered for TV, with Ethan Nicolle's hearty approval; Flute Cop has stayed Flute Cop, to better facilitate his role as the Only Sane Man; and Sockarang already has his beard despite (presumably) never encountering Bad Santa.
Running Gag: Someone puts a friendly arm around Axe Cop's shoulder, and he casually pushes it away.
Screwy Squirrel: Axe Cop and Sockarang turn into jerkasstrolls in Magic World. After hijacking the big magic show, they taunt the audience by vandalizing and then repairing the tent, and then giving everyone in the audience $100... moments before giving themselves twenty times as much.
If you're going to kill something, make sure you kill its soul, too.
At the end of "Babysitting Unibaby":
Sockarang: So Axe Cop, do you still think babies are dumb? Axe Cop: Of course I do.
Status Quo Is God: In "No More Bad Guys", Flute Cop turns into Dinosaur Soldier, Avocado Solider, and a gorilla with robo-gun fists and a red bow tie. Flute Cop is back in his orginal form in the next episode with no explanation.
In the same episode, Axe Cop kills every bad guy on Earth. That doesn't stop bad guys from showing up for the rest of the season.
There Was a Door: Seems to come with the general disregard of life and limb, such as when Liborg bursts through the wall of Axe Cop's office just to arrive at the Thanksgiving party, or when Wexter crashes through the roof of a wedding chapel to give Axe Cop a lift more immediately.
Ugly Guy, Hot Wife: Flute Cop is short, bald, and paunchy; his wife, Anita, looks like a magazine model. The show points out how good Flute Cop is with his flute.
Would Hurt a Child: Played withfor laughs; Axe Cop never commits any actual violence against Unibaby, but he's perfectly willing to abandon her to the company of cyborgs he personally programmed to punch her if she cries. Threatening to kill Unibaby is what signifies the cyborgs have crossed the Moral Event Horizon.
Played straight with Bad Santa, who enslaves/harms children and claims to have a "workshop of torture".
Would Hit a Girl: Axe Cop would, until he learns about the bad PR inherent in doing so.