Katz is an Ax-CrazySerial Killer whose actions rarely have reason or logic, but here comes one Fridge Brilliance: Katz is a cat, and several species of cats in Real Life have a potential murderer instinct and are among the few species of animals that kill because they enjoy it. Sound familiar to Katz, right?
Courage is not a lack of fear. Courage is facing your fears despite being scared.
In the episode "Courageous Cure" Eustace and Muriel are abducted by multi-armed aliens so they can get a cure for a strange disease that causes them to punch themselves. By the end of the episode, it turns out that Courage's DNA was the one with the cure. This was because the disease causes people to punch themselves and 4 legged animals such as dogs do not have arms.
Courage jumping to the conclusion that Kitty is evil and being horrified when she takes off her mask for the first time in "The Mask" makes a lot more sense when you remember the only other humanoid cat he knows is Katz, who Kitty even somewhat resembles with the same fur color. The theme of the episode deals a lot with Kitty's belief all dogs are evil because the only ones she knows are evil as well. Courage's assumptions of Kitty's true nature are partially blurred by his own encounters with Katz just like Kitty's are by her history with Mad Dog and his gang. In the end, they both learn the other really wasn't evil to begin with.
Other than that, Kitty spend most of the first half of the episode beating Courage, when all he was doing was minding his own business. His scream reaction to her identity was a TWO PARTER, if that needs any more indication.
While everyone knows Eustace refers to Courage as "Stoopid Dog!" (except for two exceptions) Courage himself never calls Eustace by name and only calls him "The Farmer". Coincidence?
In the episode "Perfect" the eel in the bathtub gives Courage a pep talk by telling him "There's no such thing as Perfect. You're beautiful just the way you are." When Courage accepts this, the perfection obsessed schoolmarm ceases to exist because there's no such thing as perfect!
The Bagges are not always the first victims to fall into the enemies traps. Katz seems to provoke this the most which is evident with the bones littered all over the hotel in "A Night At the Katz Motel", the broken machines in "Klub Katz", and questionably the candies in "Katz Kandy". There are also other villains who have shown past victims as well, such as the skulls from "The Queen Of the Black Puddle", the puppets from "The Great Fusilli", the banana peel skins from "1000 Years Of Courage", and most infamously, the monster, bones, shackles, and "help" message from "Courage In the Big Stinkin' City".
Just what did Mad Dog do that made Kitty such a depressed wreck?
Aside from keeping her best friend a prisoner? ... Possibly a lot, actually.
When you consider part of the episode was an allusion to prostitution... the mind can fill in the blanks in the backstories.
Vastabael Backjurius's plan to stop the Bagges from fixing the sun is outright Monstrous if you have knowledge of life on Earth's dependance on the sun.
That and the rest of the solar system as well...
Although the very ending of "Remembrance of Courage Past" was Played for Laughs, we now know that Courage's parents are still alive. This is of course a good thing until you realize that they have no idea what happened to Courage or that he was adopted by a kind woman. For all they know, he starved to death after being left in the garbage by himself as an infant. Now, imagine being forcibly taken from your infant child and spending the rest of your life not knowing what became of him. That's extremely depressing.
Humans live much longer than dogs. What's going to happen to Eustace and Muriel when Courage dies?
Then again, considering how old Eustace and Muriel are, it could easily be the other way around.
Eustace called in the Cajun Fox along with the rest of the villains in "Ball Of Revenge", despite the fact that the Cajun Fox episode was the only episode Eustace doesn't appear in. And he also calls in The Big Toe, even though he himself was The Big Toe.
The banana salesman appears in a later Katz episode even though he's supposed to be stuck in the next millennium.