An early villain is described as a pedophile in a graphic backstory that details how he killed a young boy. Later on, a minor villain makes sexual remarks about Koichi's teenage sister.
Okuyasu's father physically abused him when he was little. His father becomes a goop monster after Dio dies and seems to forget most of his life prior to that so Okuyasu's cool with him by the end, but it probably still counts as forgiving him.
Shizuka's parents are never confirmed to have abandoned her so it's unclear whether she truly was abandoned or simply wandered away from her parents - but she is a baby left all alone, so I'll say yes.
Keicho and Okuyasu's father physically abused his sons - Keicho later became physically and verbally abusive to Okuyasu and their father. (Episodes 3-5 of the anime; Chapters 9-18 of the manga.)
In Episode 2 of the anime and Chapter 3 of the manga Angelo is mentioned to be a rapist.
In Episode 14 of the anime and Chapter 55 of the manga, Hazamada is mentioned to want to rape one of his classmates.
Josuke's grandfather is killed by Aqua Necklace in the first arc (Episode 2 of the anime; Chapter 5 of the manga).
Keicho, Okuyasu's brother, is killed in Episode 5 of the anime and Chapter 18 of the manga.
Morioh is a seaside town, so the ocean is seen in the background of some scenes, as well as more prominently in others such as the Red Hot Chili Pepper arc.
In Episode 34 of the anime and Chapter 146 of the manga, Hayato and Kira are both naked as they bathe. None of this is presented sexually, but it's still an uncomfortable scene.
During the Nijimura Brothers arc, a character verbally and physically abuses his disabled father and his younger brother. Also, the father was shown in flashbacks to have physically abused his children before he was disabled.
A wild cat breaks into the Kawajiri residence, and Shinobi accidentally kills it. However, once Yoshikage Kira buries it, it is revived as a plant-like creature with a Stand.
Not necessarily assault, but there’s a rather creepy scene where a child is bathing and is joined by an adult man who resembles his father but is not. It is disturbing and intense to watch. Another teenage girl has her chest groped by an aesthetician briefly.
During the Let's Go To The Manga Artist's House arc, a character uses his Stand ability to attempt to force someone to immolate himself. He is saved moments later, but the fire gets very close to his face and it can be a bit intense.
{SPOILERS!}
Kira cuts off his left hand with Killer Queen to use Sheer Heart Attack as a distraction and runs off. Josuke uses his stand to restore the hand making it levitate back to Kira.
Two characters are fused with objects and left to live with that for eternity. They’re never mentioned again after it happens but... take that as you will.
Episode 10: Okuyasu's eyes get shriveled up by a stand that has possessed mineral water (not to be confused with the one that killed Josuke's grandfather) , but is seen to be benificial to him as he says that he "feels refreshed, like i slept a full 10 hours"
episodes 8+9 "Yukako Yamagishi Falls in Love" revolve around a girl kidnapping a boy and keeping him locked in her house in the middle of nowhere. She tries to win his affections but is abusive, and he is clearly frightened by her. You also see her initially abducting him from his bedroom at night.
Episode 10: A stand: Pearl Jam is consumed by Okuyasu, but it turns out to be benificial.
Episode 33-34: Although not "possessing" by going inside said person, a minor antagonist's stand, Cheap Trick, clings onto backs and gaslights victims, not being able to remove unless if another person sees said victims back so it can possess the person who saw it, but as it's forced to look to said person, this is used against the stand after Rohan contracts them, sending it to hell.
In the Nijimura Brothers arc, Keicho's Stand Bad Company, a tiny army, shoots tiny bullet holes into Josuke and Okuyasu. (Episode 4 of the anime; Chapters 11, 12 and 15 of the manga.)
correcting the other comment— Hazamada does get sick after Rohan licks the spider (and then he’s completely fine after lol), but it happens in Episode 14 on Netflix. // i’ll have to wait until i watch the scene again, but i believe Mikitaka also gets sick in the dice scene with Rohan & Josuke.
In Episode 9 of the anime and Chapter 32 of the manga, Koichi wets himself after he is forced to answer a question in order to gain access to the bathroom. No actual urine is seen, but in the next scene Koichi is stated to have wet himself and is very embarrassed about it.
While he doesn't explicitly have OCD, the primary antagonist has some behaviors hinting at obsessive-compulsive tendencies, and he has a sexual fetish that drives him to murder women for their hands.
In Episode 6 of Season 3 (Koichi Hirose (Reverb)), the main antagonist forces a protagonist's mother to feel guilty, leading her to pick up a sharp knife, take it to her neck, and loudly declare that she is going to attempt suicide. She does not, but it is a key moment in the scene.
In Episode 13 of the anime, Shizuka - a baby that Joseph and Josuke find - cries.
In Episode 20 of the anime, Shizuka once again cries when Rohan's camera flash startles her.
In Episode 29 of the anime, a baby in the street is seen crying, but stops crying when Josuke breaks his motorcycle to avoid hitting it.
Characters bleed in fights, and the fight with the rat called “Bug Eaten” is intense as a main character is almost melted into goo by the rat’s stand ability.