The interest in the measurement of the elastic properties of thin films is witnessed by the number of new techniques being proposed. However, the precision of results is seldom assessed in detail. Brillouin spectroscopy (BS) is an established optical, contactless, non-destructive technique, which provides a full elastic characterization of bulk materials and thin films. In the present work, the whole process of measurement of the elastic moduli by BS is critically analyzed: experimental set-up, data recording, calibration, calculation of the elastic moduli. It is shown that combining BS with ellipsometry a fully optical characterization can be obtained. The key factors affecting uncertainty of the results are identified and discussed. A procedure is proposed, to discriminate factors affecting the precision from those affecting the accuracy. By the characterization of a model transparent material, silica in bulk and film form, it is demonstrated that both precision and accuracy of the elastic moduli measured by BS can reach the 1% range, qualifying BS as a reference technique.