I think he's poorly implemented.

His eyes don't look where he's "looking". His movements and mannerisms, facial expressions don't match what he is doing or saying.

He stands there like a block of wood but sounds like he is shouting at the top of his lungs.

Yes, some will read this ands ay "well he's mad, he's supposed to be jarring" and such, but I do not believe that holds water in this case. He is not animating or behaving correctly with respect to where he is looking or the tone of his voice.

He isn't emoting properly with regards to the rage he expresses sometimes. His face remains the same with the boring straight white eyes looking to the side of you.

It's a minor thing (because most of us are done with those quests now), but he could do with a large improvement.

I'm disappointed with his outward appeareance in general. From
one game to the next he always looked completely different while
still being an old man with a beard. His face and clothes always
changed completely, so I hoped to see an entirely differently
looking Sheogorath, but they basically retained his appeareance
from Skyrim except for his left sleeve. They could have gone so
wild with his design, yet they just changed the sleeve. Everything
would make sense with him, he could have had blue eyes with x-shaped
pupils, silver lipstick , purple pants with green hearts and other weird
and absurd fashion craziness (preferably something that I did not design,
as the examples above clearly show that I would absolutly
have no future as a fashion designer, I just wanted to point out that
you can go wild on his appeareance as long as you keep him an old
man with a beard, other people can surly give him a fantastic and
pretty new design).

I also agree with his movements and facial expressions
not fitting to his actions and speech. It looked better in Oblivion,
where you could see an immediate change in his face as he changed
from anger to joy to all kinds of emotions within the same speech.
In ESO he mostly just stands around and tries to move as little as
possible, but it doesn't fit him at all. He hates Jygallag because
Jygallag makes everything orderly and static, so why would you
expect him stand around with the same face all the time?
He is crazy, so you should see him laughing hysterically, shouting
loudly, dancing etc, changing from one action to the next within few moments.
Look at the Wabbajack, it depicts him withall kinds of emotions, so you should
actually see him doing thatas he is known for his random emotional
outbreaks and standing around like a tree does not qualify as an emotional outbreak to me.

On the other hand, what I do actually like about him in ESO is that
he is not depicted as the friendly old man he was in Oblivion and Skyrim.
For once he is not the charmingly weird uncle who all people love but
a psychopath who shows his murderous side. He sets a guy on fire for
his amusement, sends crazy people after you while laughing as you slaughter
them and turns Valaste slowly crazy ,which she calls "a fate worse than death"
if I remember correctly, just to torture Shalidor. I also like the fact that he sends
you to the Dementia side of the Shivering Isles for the Mages Guild quests as
it really shows that this time, you get a taste of his unfriendly side without cheese
for anybody.

To sum it up: I like how he is depicted storywise, but his outward appeareance and
movement could have been way, way better.

Must not do it can't stop. So it's time to cut the cheese?

Yes please, this Khajiit wants ucle Leo to have cat's eyes