The Collaborative International Dictionary of English v.0.48:

Light-minded \Light"-mind`ed\ (l[imac]t"m[imac]nd`[e^]d), a.
   1. Unsettled; unsteady; volatile; not considerate.
      [1913 Webster]

   2. showing inappropriate levity. [WordNet sense 1]

   Syn: flippant.
        [WordNet 1.5] -- Light"-mind`ed*ness, n.
        [1913 Webster]

WordNet (r) 3.0 (2006):

light-mindedness
    n 1: inappropriate levity; "her mood changed and she was all
         lightness and joy" [syn: flippancy, light-mindedness]