The Collaborative International Dictionary of English v.0.48:

Gaudiness \Gaud"i*ness\, n.
   The quality of being gaudy. --Whitlock.
   [1913 Webster]

WordNet (r) 3.0 (2006):

gaudiness
    n 1: tasteless showiness [syn: flashiness, garishness,
         gaudiness, loudness, brashness, meretriciousness,
         tawdriness, glitz]
    2: strident color or excessive ornamentation [syn: garishness,
       gaudiness]

Moby Thesaurus II by Grady Ward, 1.0:

129 Moby Thesaurus words for "gaudiness":
   Barnumism, affectation, apparent character, appearances,
   arsenic green, bedizenment, beggarliness, big talk, blatancy,
   brazenness, cheapness, clashing colors, coarseness, color clash,
   colorfulness, contemptibleness, convolution, crassness, crudeness,
   crudity, crumminess, dash, dazzle, dazzlingness, despicableness,
   display, earthiness, exteriors, external appearance, externals,
   extravagance, extravaganza, extravagation, facade, flagrancy,
   flamboyance, flashiness, flatulence, flatulency, front,
   fulsomeness, gaiety, garishness, gaudery, glare, glitter,
   gorgeousness, grandiloquence, grandioseness, grandiosity,
   grossness, high-flown diction, inflatedness, inflation,
   jaundiced yellow, jauntiness, jazziness, lexiphanicism, luridness,
   magniloquence, meanness, mere externals, mere rhetoric,
   meretriciousness, meritlessness, miserableness, obscenity,
   obtrusiveness, orotundity, ostent, ostentation,
   ostentatious complexity, outward appearance, outward show,
   paltriness, panache, pitiableness, pitifulness,
   platitudinous ponderosity, polysyllabic profundity, pomposity,
   pompous prolixity, pompousness, pontification, poorness,
   pretension, pretentiousness, prose run mad, public image, rawness,
   rhetoric, rhetoricalness, ribaldry, roughness, rudeness, sadness,
   screaming color, sensationalism, sententiousness, shabbiness,
   shamelessness, shocking pink, shoddiness, show, showiness,
   sorriness, speciousness, sportiness, stiltedness, superficiality,
   surface appearance, surface show, swelling utterance,
   swollen phrase, swollenness, tall talk, tawdriness, tortuosity,
   tortuousness, tumidity, tumidness, turgescence, turgidity,
   unworthiness, vain show, vileness, vulgarness, worthlessness,
   wretchedness