There are wolves in the Bloodmoon DLC that are considered enemies that can be killed, as well as undead "bonewolves" that are mutilated wolves that attack you. While not explicitly dogs, the Nix-Hounds in base game Morrowind and Durzogs in the Tribunal DLC are considered "dog-like" in nature and are enemies that can be killed.
In the Temple questline, it's mandatory for the player to taunt a Daedra to proceed. Doing so causes the Daedra to threaten that they will explicitly sexually assault the player and attacks them.
It's not misgendering necessarily, but the word 'hermaphrodite' is used in game to describe Vivec, an intersex character who primarily presents as male, which could be seen as dated.
Racism and xenophobia is a central component in the game's narrative. Many Dunmer will often belittle your character for being an outsider to the island the game takes place on, and slavery of the beast races is seen as acceptable by their society.
Although not in-game, there is a well known illustration by game writer and artist Michael Kirkbride that is tied to the game's narrative, showing the amputation of a character's feet, the skinning of their face and the removal of their heart from their chest.
In the first 10 minutes of the game, it is likely you will find a wizard who tries to use a spell to fly, but fails and falls to his death right in front of you.