The Collaborative International Dictionary of English v.0.48:

Imbroglio \Im*brogl"io\, n.; pl. Imbroglios. [Written also
   embroglio.] [It. See 1st Broil, and cf. Embroil.]
   1. An intricate, complicated plot, as of a drama or work of
      fiction.
      [1913 Webster]

   2. A complicated and embarrassing state of things; a serious
      misunderstanding or disagreement, especially one that is
      bitter.
      [1913 Webster +PJC]

            Wrestling to free itself from the baleful imbroglio.
                                                  --Carlyle.
      [1913 Webster]

WordNet (r) 3.0 (2006):

imbroglio
    n 1: an intricate and confusing interpersonal or political
         situation [syn: imbroglio, embroilment]
    2: a very embarrassing misunderstanding

Moby Thesaurus II by Grady Ward, 1.0:

76 Moby Thesaurus words for "imbroglio":
   altercation, argument, bicker, bickering, bind, blood feud, brawl,
   broil, clutch, complication, contention, controversy, crunch,
   dispute, donnybrook, donnybrook fair, embarrassing position,
   embarrassment, embroilment, falling-out, feud, fight,
   fine how-do-you-do, fliting, fracas, fuss, hell to pay, hobble,
   hot water, how-do-you-do, jam, logomachy, mess, miff, mix, morass,
   open quarrel, parlous straits, pass, pickle, pinch, plight,
   polemic, predicament, pretty pass, pretty pickle,
   pretty predicament, quagmire, quarrel, quicksand, row, scrape,
   sharp words, slanging match, slough, snarl, spat, spot, squabble,
   squeeze, stew, sticky wicket, strait, straits, strife, swamp, tiff,
   tight spot, tight squeeze, tightrope, tricky spot, tussle,
   unholy mess, vendetta, words, wrangle