Adam and Eve Plot: This happened at the end of the episode that spoofed Noah's Ark. After eating all of the food on the Ark, chewing off the horns of the unicorns, and other disasters, Hollywood/Noah finally gets sick of the dogs and tries to throw them overboard. Suddenly the storms passes and an overjoyed Noah shouts "Drop anchor, brethren!" Big Dog then throws the anchor in the air, sinking the ship. The Dogs end up swimming to a nearby island. Thousands of years later all of civilization looks like the two stupid dogs. It's probably best not to think about which dog was the "Adam" and which was the "Eve".
All Just a Dream: Played in an interesting way in one episode. They thought they were in a dream, and tried to wake up from it no matter what. It lead to alot of pain at one point.
Boot Camp Episode: They were sent to "cartoon boot camp" and given the names "Hammy & Loafy".
Catch Phrase: Hollywood's "Well, ain't that cute... BUT IT'S WRONG!!" Subverted exactly once in the series — Hollywood even broke the Fourth Wall to deliver a Lampshade Hanging.
Genre Savvy: Even stupid dogs can have a bout of Genre Savviness. The third time they meet Red the little dog tries to get away from her calling her an "evil little girl" after the last two times they met ended badly for them. Of course they are once again tempted to follow Red by the dog food she is carrying.
Incidentally, this was also the episode that actually ends well and they all lived happily ever after.
In an episode where the dogs are trying to find a shoe, they make a stop at a strip club. Although the stripper is in silhouette, she very explicitly removes her bra.
Take it off! Take off your shoe!
In one episode, a boy brings the dogs to school for show and tell. During his presentation, the boy mentions that the dogs are male, and to prove it he picks up the little dog by the hind legs and pretty much flashes the whole classroom. The moment was made worse by the fact that while most of the students looked horrified, the female student that recieved a closeup was delighted by the sight.
How embarrassing, they saw me.
There was also an episode that was a Take That at the Brady Bunch where the expy of Greg and Marsha got into an argument and their parents told them to kiss and make up. They started making out.
"And he's got nerve calling me "weenie dog"! So I bit him. What would you do? I mean, he stuck it in my face!"
In the episode Las Pelotas, Little Dog ricochets a tennis ball from off of Big Dog's lower abdomen. Little Dog says "Balls" prompting Big Dog to reply "Yeah, I know".
The Secret Squirrel segment had some going on too. the Chief once asked a woman how she felt about "undercover work".
In one episode, Hollywood asks Little Dog if he likes parrots and Little Dog says incredulously "In what way?"
Groin Attack: Big Dog and Hollywood are victims to this trope.
Occasionally - for example, a kitten getting chewed up (no red gore, mind you) and spat out, and a quarter forcefully inserted into the bigger dog's cranium.
Idiosyncratic Episode Naming: Super Secret Secret Squirrel named almost all its episodes after that week's Big Bad (e.g. "Queen Bea," "Greg," "Doctor O").
Most Definitely Not a Villain: Little Dog's plan to distract a cat was using a cat puppet. "Hey, cat! Hey! Look at me! I'm a cat, not a puppet! And we can be friends, you can trust me, because I'm a cat, not a puppet... and definitely not a dog."
Naked People Are Funny: In the episode "Stunt Dogs", when Hollywood accidentally gets his loin cloth torn off.
Hollywood: now wasn't that cute... BUT IT'S— *revels to have a pineapple covering his crotch*
No Name Given: The eponymous dogs. They are called Big Dog and Little Dog. Though in "Cartoon Canines", they are called Loafy and Hammy, respectively. But in "Love", a female hamster calls Big Dog Jonathan. In "At the Post Office", in order to play it safe, Little Dog decided to fill a draft form and didn't know his own name. Based on Big Dog's last answer to the question about his name, Little Dog registerem his name as Ida Know.
Perma Stubble: Hollywood, even in the episodes where he plays a woman.
Pie Eyed: Used in "Hobo Hounds", which was made to look like an old silent cartoon.
Puff of Logic: Secret defeats a living quark by showing him via a dictionary that he is purely a hypothetical particle and thus doesn't exist.
Running Gag: The piece of corn randomly appearing.
The beginnings of the Red episodes have quite a few gags, such as Big Dog getting covered in flowers and Little Dog offering the same dead squirrel in varying stages of decay.
The music played during the giant door in "Cookies, Ookies, Blookies" sounds like "Thus Spoke Zarathustra".
"Cartoon Canines" has a lot of homages to other cartoons.
Drill Sergeant: No cutesy in my corps, only classic funny cartoons. You know, lots of butt jokes! Too Beanie! Too out there! Too in there! Too diseased!
Also in Cartoon Canines, in a in-show segment parodying the likes of [[Tom&Jerry]], a large cat (I think) sits on the Little Dog, saying "Did I do that?", then the little dog, who is now green-skinned, muscular and very pissed off proceeds to left the cat off of him.
The naming scheme of the Red sequels mimic that of the Star Wars original trilogy.
"Cartoon Canines", a very slow paced episode portraying the dogs as Animated Actors, who showcase little to none of their trademark stupidity, and the episode concludes with a Big Lipped Alligator Moment.
Hobo Hounds is a tribute to the silent era black-and-white cartoons of the 1920s.
One episode in Vegas has the dogs only want to go to a casino's hot dog buffet. However, Big Dog wins a huge jackpot in the slots prompting the casino's owner to force them to gamble in order to get his money back, but they end up nearly draining the casino dry of money instead. Eventually the Big Dog loses after the owner agreed to give the two all the hot dogs from the buffet in exchange.
During the The Price Is Right spoof the little dog keeps trying to lose every round because he wants the consolation prize box of doggy treats. Naturally he wins every round. Taken to a truly ridiculous extreme when the dog sabotages the final round to avoid winning the grand prize — a luxury car. The host calls him out on cheating and makes him take the car.
Why Do You Keep Changing Jobs?: Hollywood. Taken to the extreme in the "Pie In The Sky" episode where the dogs visit every department of a store, and the salesperson in each and every one is just Hollywood in different clothes.
Actually, it was revealed in the end of episode that the sales people are just Hollywood look-alikes instead of one person wearing different clothes.
He's not the only one. The store clerk seems to be employed by every existing store in the show as well.