It is becoming increasingly important to understand the uncertainties of nuclear mass model calculations and their limitations when extrapolating to driplines. In this paper we evaluate the parameter uncertainties of the Duflo-Zuker (DZ) shell model mass formulae by fitting to the latest experimental mass compilation AME2012 using the least square and minimax fitting procedures. We also analyze the propagation of the uncertainties in binding energy calculations when extrapolated to driplines. The parameter uncertainties and uncertain propagations are evaluated with the help of the covariance matrix thus derived. Large deviations from the extrapolations of AME2012 are seen in superheavy nuclei. A simplified version of the DZ model (DZ19) with much smaller uncertainties than that of DZ33 is proposed. Calculations are compared with results from other mass formulae. Systematics on the uncertainty propagation as well as the positions of the driplines are also presented. The DZ mass formulae are shown to be well defined with good extrapolation properties and rather small uncertainties, even though some of the parameters of the full DZ33 model cannot be fully determined by fitting to available experimental data.