These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Awesome Music: The theme song, which is often considered the best part of the show. Even people who hate the show agree that it's good.
Dude, Not Funny!: Cat is always the one who suffers the most from his crazy friends/enemies, but especially Dog's dog-like antics. It's even sadder how Dog just watches as his brother is brutally skinned alive several times without doing anything.
Ear Worm: Cat-Dog, Cat-Dog! Alone in the world is a little Cat-Dog!
"A pretty little piece of paradise / That's a-where I wanna be..."
The Scrappy: Winslow and Rancid Rabbit appear to be this, since they almost always ruin CatDog's day - in Winslow's case, mostly because he's a complete dick. For Rancid his recurring appearance and mean attitude is seen to be annoying.
Cliff of the Greasers, as well. Shriek is more of a Base Breaker, as she has a few good moments with Dog, and Lube averts this, due to having a few episodes in which he is not an antagonist (and a lot of other instances of being too stupid and ineffectual to be malicious otherwise). Cliff, however, is just a Jerk Ass (though to compensate, he arguably has the most frequent moments as The Chew Toy).
There are quite a few fans who hate Lola, some even comparing her to Scrappy-Doo.
They Wasted a Perfectly Good Plot: The Great Parent Mystery. It had a lot of build up to it, and generated some interest into the identity of CatDog's parents. Only it turns out that the bigreveal was that we get to see CatDog's adoptive parents. One could imagine a few people being annoyed by this.
Unfortunate Implications: The Greasers constant beatings of CatDog, especially Cat reeks of racism and/or general prejudice.
That may have been intentional, though.
Indeed, one episode implies that they pick on CatDog because they're two-headed.
Values Dissonance: One of Winslow's lines directed toward Cat, which goes "How 'bout I sock you right in the pussnote As in 1940s slang for "face", Puss!note As in general slang for cat". They could get away with it in the 90s, but given the term's change in useage over the years, it's a miracle that this line was able to stay in on reairings.