Spectral albedo of the snow surface in the visible/near-infrared range has been measured for 3 years by an automatic spectral radiometer installed at Dome C (75°S, 123°E) in Antarctica in order to retrieve specific surface area (SSA) of superficial snow. This study focuses on the uncertainties of the SSA retrieval due to the instrument deficiencies and issues related to data processing. We find that when the solar zenith angle is high, the main source of error is the imperfect angular response of the light collectors. This imperfection introduces a small spurious wavelength-dependent trend in the albedo spectra which greatly affects the SSA retrieval. By modeling this effect, we show that for typical snow and illumination conditions encountered at Dome C, retrieving SSA with an accuracy better than 15% (our target), requires the slope of this trend not to exceed 2% between 400 and 1100 nm. Such a small slope can be achieved only by i) careful design of the collectors, ii) an ad hoc correction of the spectra using the actual measured angular response of the collectors, and iii) for solar zenith angles less than 75°. The comparison of the retrieved SSA with independent measurements made with an optical device operating at 1310 nm confirms the presence of a sharp and recurrent vertical gradient of SSA in the uppermost centimeter at Dome C, which challenges the assessment of the absolute accuracy from independent measurements. Nevertheless, with three-fold variations of SSA during the summer seasons, we conclude that the retrieved SSA is accurate enough to provide a detailed picture of the October-March evolution of the surface snow at Dome C.