We present results for a time-dependent Dalitz plot measurement of CP-violating asymmetries in the mode B-0 -> pi(+)pi(-)pi(0). The data set is derived from the complete sample of 471 x 10(6) B (B) over bar meson pairs collected with the BABAR detector at the PEP-II asymmetric-energy e(+)e(-) collider at the SLAC National Accelerator Laboratory operating on the Upsilon(4S) resonance. We extract parameters describing the time-dependent B-0 -> rho pi decay probabilities and CP asymmetries, including C = 0.016 +/- 0.059 +/- 0.036, Delta C = 0.234 +/- 0.061 +/- 0.048, S = 0.053 +/- 0.081 +/- 0.034, and Delta S = 0.054 +/- 0.082 +/- 0.039, where the uncertainties are statistical and systematic, respectively. We perform a two-dimensional likelihood scan of the direct CP-violation asymmetry parameters for B-0 -> rho(+/-)pi(-/+) decays, finding the change in chi(2) between the minimum and the origin (corresponding to no direct CP violation) to be Delta chi(2) = 6.42. We present information on the CP-violating parameter alpha in a likelihood scan that incorporates B-+/- -> rho pi measurements. To aid in the interpretation of our results, statistical robustness studies are performed to assess the reliability with which the true values of the physics parameters can be extracted. Significantly, these studies indicate that alpha cannot be reliably extracted with our current sample size, though the other physics parameters are robustly extracted.