The interest in the measurement of the elastic properties of thin films is witnessed by a 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 setup, data recording, calibration, and 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 1% range, qualifying BS as a reference technique.