Dogs are killable. Some don't attack the player until attacked themselves, and others will attack the player on sight. The Shivering Isle expansion has a dog companion the player can get that is a walking undead corpse.
There is one character involved in the Dark Brotherhood questline who displays symptoms of PTSD originating from an event that happened in their childhood.
At least two NPCs will track you down and attempt to kill you. This can be avoided by not doing their quests.
Also it’s revealed that a certain NPC is stalking other people.
It is revealed during a Dark Brotherhood quest that an NPC had his own mother murdered. The killing is not shown in game, but her corpse will come to life and attack you later on.
Mountain Lions may appear as enemies and can be killed, also some NPCs may be of the Khajiit race and they are basically cat-people, they can also be killed
There are several instances where a pet can be killed or has died
For example, there is a quest in the Fighter's guild where a woman's pet rats are killed by mountain lions
Depending on what race and sex the player choose (namely female Nords or Dark Elves,) the Dark Elf prisoner across the hallway will make vulgar comments about them, implying that if they were in the same cell, he would r*pe the player. This never occurs, but the threat is still gross.
Later on, this prisoner can be killed for money during the Dark Brotherhood questline.
Dead, mutilated bodies can be found strung up all across Cyrodiil, particularly in vampire dens and in the Deadlands
One particular case of gore is during the Dark Brotherhood questline, where a character is shown having been mutilated (limbs/organs and chunks of flesh missing plus lots of blood)
at least one quest line I know of involves an argonian woman being kidnapped for a cultist ritual. another argonian priest is found tied up for sacrifice by a daedric sect as well. there's probably more.
The Shivering Isles DLC has two major zones, named Mania and Dementia, and mental illness (as well as a more general "madness") is a significant theme. Many characters presumed to be "mad" are also violent. Sheogorath, the Daedric Prince of Madness, is unstable, chaotic, and can be quite antagonistic.
The Fighter's Guild plotline has a character who dies towards the end of it. Reading his diary (which is found on his corpse) heavily implies that he was in a relationship with another man, meaning you don't even find out that he was gay until after his death.
Tamriel has no Septim anymore, leaving the entire Empire with no ruler. Basically the whole world is in upmost chaos as the neighboring provinces take advantage of the now weakened Empire.
The player can drown. Also significantly, there is a mage's guild quest that involves a character that was murdered after picking up an enchanted item in a well that paralyzed them and caused them to drown. The player can pick this item up too and suffer the same fate.
The Shivering Isle expansion has a dog companion the player can get that is a walking undead corpse.