Decoherence is not enough to explain why we don't see quantum weirdness. It has to be coupled with some additional assumptions, called "
interpretations of quantum mechanics". Some interpretations are:
(1) textbook (eg. Landau & Lifshitz, Peres): quantum mechanics as a theory always requires the division of the universe into classical and quantum. We only see classical results, which by definition are irreversible, definite marks. In this view quantum mechanics may be incomplete.
(2) Bohmian mechanics (eg.
http://arxiv.org/abs/quant-ph/0308039) is an example of a theory or interpretation that completes non-relativistic quantum mechanics by postulating hidden variables. In this interpretation, there are truly particles with definite positions, but there is a randomness in their positions called quantum equilibrium, analogous to the randomness of particles in thermodynamic equilibrium.
(3) Many-worlds in which all definite outcomes occur, and the universe splits into distinct realities. If this interpretation works, then it is a logical possibility that quantum mechanics is complete. It is not yet clear if this definitely works, but an account that seems very convincing is in Wallace's http://users.ox.ac.uk/~mert0130/books-emergent.shtml.