Tracer particle microrheology using diffusing wave spectroscopy-based microrheology is demonstrated to be a useful method to study the dynamics of aqueous Pluronic™ F108 solutions, which are viewed as solutions of repulsive soft spheres. The measured zero-shear microviscosity of noncrystallizing micellar dispersions indicates micelle corona dehydration upon increasing temperature. Colloidal sphere thermal motion is shown to be exquisitely sensitive to the onset of crystallization in these micellar dispersions. High temperature dynamics are dominated by an apparent soft repulsive micelle-micelle interaction potential indicating the important role played by lubrication forces and ultimately micelle corona interpenetration and compression at sufficiently high concentrations. The measured microscopic viscoelastic storage and loss moduli are qualitatively similar to those experimentally observed in mechanical measurements on colloidal dispersions and crystals, and calculated from mode coupling theory of colloidal suspensions. The observation of subdiffusive colloidal sphere thermal motion at short time-scales is strong evidence that the observed microscopic viscoelastic properties reflect the dynamics of individual micelles rather than a dispersion of micellar crystallites.