The Collaborative International Dictionary of English v.0.48:

Dimness \Dim"ness\, n. [AS. dimness.]
   1. The state or quality ? being dim; lack of brightness,
      clearness, or distinctness; dullness; obscurity.
      [1913 Webster]

   2. Dullness, or want of clearness, of vision or of
      intellectual perception. --Dr. H. More.

   Syn: Darkness; obscurity; gloom. See Darkness.
        [1913 Webster]

WordNet (r) 3.0 (2006):

dimness
    n 1: the state of being poorly illuminated [syn: dimness,
         duskiness]
    2: the property of lights or sounds that lack brilliance or are
       reduced in intensity [syn: dimness, subduedness]
    3: the quality of being dim or lacking contrast [syn: dimness,
       faintness]

Moby Thesaurus II by Grady Ward, 1.0:

133 Moby Thesaurus words for "dimness":
   adiaphanousness, anemia, ashiness, asininity, bad light,
   bleariness, blockishness, bloodlessness, blur, blurriness,
   boobishness, boorishness, bovinity, cadaverousness, chloranemia,
   cloddishness, cloudiness, crassness, crudeness, darkishness,
   darkness, darksomeness, deadness, deathly hue, deathly pallor,
   decrescendo, defocus, denseness, density, dim, dim light,
   dim-wittedness, doltishness, drabness, dull-wittedness, dullardism,
   dullness, dumbness, duncery, dusk, duskiness, duskness,
   exsanguination, fadedness, faintness, fairness, feebleness,
   filminess, flatness, fogginess, fuzziness, gentleness, ghastliness,
   gloaming, grossness, haggardness, half-light, half-visibility,
   haziness, hebetude, hypochromia, hypochromic anemia,
   imperviousness to light, indefiniteness, indistinctness,
   indistinguishability, intransparency, lack of sparkle, lackluster,
   lethargy, lifelessness, lightness, lividness, loutishness,
   low profile, lowness, lumpishness, lusterlessness, mat, mat finish,
   mistiness, muddiness, murk, murkiness, ninnyism, oafdom,
   oafishness, obscurity, obtuseness, opacity, opaque, opaqueness,
   paleness, pallidity, pallidness, pallor, partial darkness,
   pastiness, prison pallor, roil, roiledness, sallowness, semidark,
   semivisibility, shadowiness, sickliness, sickly hue,
   simpletonianism, slowness, sluggishness, soft focus, softness,
   somberness, sottishness, stolidity, stupidity, subaudibility,
   subduedness, thick-headedness, thick-wittedness, turbidity,
   turbidness, twilight, uncertainty, unclearness, unplainness,
   unteachability, vague appearance, vagueness, wanness, weakness,
   wrongheadedness, yokelism