Parameter estimates of GW150914 were obtained using Bayesian inference,based on three semi-analytic waveform models for binary black holecoalescences. These waveform models differ from each other in theirtreatment of black hole spins, and all three models make some simplifyingassumptions, notably to neglect sub-dominant waveform harmonic modesand orbital eccentricity. Furthermore, while the models are calibrated toagree with waveforms obtained by full numerical solutions of Einstein’sequations, any such calibration is accurate only to some non-zero toleranceand is limited by the accuracy of the underlying phenomenology, availability,quality, and parameter-space coverage of numerical simulations. This papercomplements the original analyses of GW150914 with an investigation of theeffects of possible systematic errors in the waveform models on estimatesof its source parameters. To test for systematic errors we repeat the originalBayesian analysis on mock signals from numerical simulations of a series ofbinary configurations with parameters similar to those found for GW150914.Overall, we find no evidence for a systematic bias relative to the statisticalerror of the original parameter recovery of GW150914 due to modelingapproximations or modeling inaccuracies. However, parameter biases arefound to occur for some configurations disfavored by the data of GW150914:for binaries inclined edge-on to the detector over a small range of choices ofpolarization angles, and also for eccentricities greater than ∼0.05. For signalswith higher signal-to-noise ratio than GW150914, or in other regions of thebinary parameter space (lower masses, larger mass ratios, or higher spins),we expect that systematic errors in current waveform models may impactgravitational-wave measurements, making more accurate models desirablefor future observations.