YMMV considering character development is involved ,but even then not all of said abusive qualities are straight up quelled (particularly favoring one child over the other)
The character named Sargent Hatred is a known pedophile and there are frequent references made to this, as well as implications that he had abused the main two brothers when they were minors.
In the beginning Dr. Venture is addicted to diet pills, this stops as seasons go on. Action Johnny was a drug addict and this is a main point for his character until he recovers in S4E6. The Pirate Captain uses tranquilizers on himself which is implied to be a drug to him, he is forced to quit.
Dr. Venture is initially addicted to diet pills, this later ceases. Action Johnny is addicted to drugs, he recovers. The Pirate Captain is addicted to tranquilizing himself, he recovers.
In S2E4, a character is put in a choke hold as a way to get him to give up information. In the season 7 finale, a character's windpipe is crushed, rendering him unable to speak.
There’s a recurring character that is a pedophile, one seeking treatment mind you but still occasionally makes comments sexualizing young boys. The show in general also has quite a few instances of minors in sexual situations
Most of the time characters are only referred to by aliases/chosen names but there are occasionally jokes involving characters being called by their birth-given name. For example Rusty is almost never called Thaddeus and the Monarch is rarely called Malcolm
There’s a recurring character named Augustus St Cloud that collects numerous pop culture artifacts and has little to no regard for handling them with care
There is a character named Radical Left that’s a parody of Batman’s Two-Face...but in an interesting twist it’s revealed that it’s not due to DID they’re two people that somehow got fused together. There is admittedly still a joke about it regarding Hank’s alter egos in that same season albeit partially at the expense of the movie Split
Cross dressing is sometimes played for laughs. Dr. Girlfriend is subjected to transphobic jokes and rumors in the early seasons, but this ends by Season 3. Hunter Gathers also has a transphobic storyline at one point not helped by the fact that he de-transitions back into a man
The character of Dr. Girlfriend is a woman with a very deep voice. She is often misgendered in the early seasons and other characters will often discuss her sex or gender in a transphobic manner.
Somewhat transphobic content in the early seasons. And in general the show relies on stereotypes even if in their defense it’s usually to make fun of the racism of the 1960’s and 70’s action cartoons they’re parodying. Some are a bit harder to defend than others though
Brock disguised himself as an Indian in S3E2 and in the Halloween special there are a couple of characters sewn together try to cosplay the Thing With Two Heads at a party but at least in that case people call them out
A teenage girl tricks an adult man into sex by lying about her age, and when she grows up she even seduces a teenage boy (bonus ick points for how said boy is also technically her stepson)
A man has a relationship with a Sasquatch and a shrunken man mentions have been “r*ped” by ants. An anthropomorphic gorilla also tries to sexually assault a male human
Sgt Hatred’s ex-wife Princess Tiny Feet is heavily into it to the point of it being her only major defining character trait. There’s also one part in S4E14 where Dr Mrs Monarch and 21 pretend that they’re having a session in order to get some of the other henchmen out and avoid being discovered. Later on in Season 6 we also see Brock engage in this with Wariana as part of his character arc
Notoriously ended on a cliffhanger although fortunately does have a continuation in film form after being uncancelled. UPDATE: said film is much happier in comparison