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Free electron LASer in Hamburg is the first free electron laser user facility operating in the vacuum ultraviolet and soft X-ray wavelength range. Many user experiments require knowledge of the spatial and temporal coherence properties of the radiation. In this paper, we present a theoretical analysis of the coherence properties of the radiation for the fundamental and for the higher odd frequency harmonics. We show that temporal and spatial coherence reach their maxima close to the free electron laser (FEL) saturation but may degrade significantly in the post-saturation regime. We also find that the pointing stability of short FEL pulses is limited due to the fact that nonazimuthal FEL eigenmodes are not sufficiently suppressed. We discuss possible ways for improving the degree of transverse coherence and the pointing stability. [ABSTRACT FROM AUTHOR]