  Particularities of the statistical mixed phase model for describing the
deconfinement phase transition and physics constraints on the model parameters,
are discussed. The modifications proposed concern an improved treatment of
hadron-hadron interactions within the nonlinear mean-field model of nuclear
matter and an inclusion of the one-gluon exchange correction into the
quark-gluon sector of the mixed phase thermodynamic potential. It is shown that
the mixed phase model successfully reproduces both the available lattice data
on the QCD deconfinement transition and thermodynamic characteristics of hadron
systems evaluated within the modern models. The 'softest point' of the equation
of state resulting in a possible formation of a long-lived fireball in nuclear
collisions (the 'softest point' effect) is analyzed. The obtained results are
confronted with the data on the two-phase model. Some manifestation of the
mixed phase formation and deconfinement transition is estimated in fireball
expansion dynamics. We discuss experimental possibilities of observing the
softest point effect as a signal of the deconfinement phase transition.
