Mainly played for laughs.
The Zombies look a little worse for wear and suffer a number of physical humiliations. They're clearly rotting, and one drops an ear.
An extended gag involves Norman struggling to retrieve a book from a man's freshly dead corpse.
Others zombies lose arms or are shot through the guts during battles with the living. (Nothing Graphic)
We can see straight through one zombie's abdomen. And another loses his head, literally, when hit by a car. Their dead appendages are still quite active, naturally. This is done more comically than gory.
A zombie runs into a door and gets her teeth stuck.
A zombie's face seems to be sagging off his jawbone rather grotesquely.
Villagers assault zombies with all sorts of makeshift weapons and try to burn down city hall, with living people inside.
A witch's powers are quite frightening and dangerous. She causes wooden thorns to spike from the ground, nearly impaling Norman, and hurls painful bolts of magical energy at him.
Norman mentions that he's watching violence when describing a zombie movie.
Keep in mind it's animated so detail is limited.