In this paper, the direction of arrival (DOA) localization of spatially distributed sources impinging on a sensor array is considered. The performance of the well known MUSIC estimator is studied in the presence of model errors due to angular dispersion of sources. Taking into account the coherently distributed source model proposed in [1], we establish closed-form expressions of the DOA estimation error 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 MUSIC for coherently distributed sources.