A notation:
I posted this same exact bug over a year ago, and surprise, surprise! It was never fixed. So ZOS, can you get your model, animation team off their...well you know what, and get them to fix this damn horrible atrocity of a visual design. It's been over a year already. So without further ado, I will copy and paste my old post:
Dear ZOS,
I get it, ok. You hate Argonians. You give us helmets that don't necessarily fit us, and on top of that, poor animations for our character models. More specifically, whenever yielding a 1 handed weapon + shield (does NOT occur with any other weapon combinations thus far), the eyeball pops out of our eye sockets when the iris shifts from right to left. I'm starting to wonder if Argonians now suffer from Graves Disease. Please fix this.
@ZOS_GinaBruno @ZOS_JessicaFolsom, please pass this onto the character model/animation team.
P.S.: This bug also occurs during the furious personality, when the character starts doing the shifty eye, looking right to left, left to right.
Edited for brevity.