How bad is yellowness of the eyeballs?

Depends on cause: The eyes may appear yellow for many reasons. Jaundice, or a high concentration of blood breakdown products not being cleared by the liver, will result in yellow eyes and skin. This should be evaluated by an internist. Sun damage, resolving subconjunctival hemorrhage, and racial differences in tissue pigmentation can also cause yellow eyes, but are generally not harmful. See an ophthalmologist.