Impaired adduction when attempted to gaze contralaterally to affected eye
Contralateral eye abducts with nystagmus
Divergence of eyes results in horizontal diplopia when looking contralateral (to affected eye)
Convergence remains intact (differentiates CN III palsy from<unk>
Internuclear ophthalmoplegia
Multiple sclerosis 
Nystagmus
Stroke
Ocular palsy
Malignancy located in brainstem and 4th ventricle
Facial paralysis
CN III palsy would show additional deficit including weakness of elevation, ptosis, pupil dilation