Are you rendering sub-frames and are your eyeballs rendering in the same render as the rest of the character....I had a simiar problem once with artifacts on a character's face that had to move with a live-action character....turned out that the two different pieces of footage/render simply wern't synced propperly. I had the problem again just as you have now, turned out that switching off sub-frame rendering (in this case in renderman) solved the problem.