In this paper, the direction of arrival (DOA) localization of spatially distributed sources impinging on a sensor array is considered. The performance of the Distributed Source Parameter Estimator (DSPE) is studied in the presence of model errors due to the angular distribution shapes of the sources. Taking into account the coherently distributed source model proposed in Valaee et al.[1], we propose a definition of angular dispersion which makes DSPE robust to the angular distribution shapes of sources, and establish closed-form expressions of the DOA estimation bias and mean square error (MSE) due to both the model errors and the effects of a finite number of snapshots. The analytical results are validated by numerical simulations and allow to analyze the performance of DSPE for coherently distributed sources. The results also show the advantage of DSPE for the localization of spatially distributed sources even if the source angular distribution shape is not exactly known.