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