UV, optical, and near-IR spectra of Vega have been combined to test our understanding of stellar atmospheric opacities and to examine the possibility of constraining chemical abundances from low-resolution UV fluxes. We have carried out a detailed analysis assuming local thermodynamic equilibrium (LTE) to identify the most important contributors to the UV continuous opacity: H, H-, C I, and Si II. Our analysis also assumes that Vega is spherically symmetric and that its atmosphere is well described with the plane-parallel approximation. By comparing observations and computed fluxes, we have been able to discriminate between two different flux scales that have been proposed, the IUE-INES and the HST scales; we favor the latter. The effective temperature and angular diameter derived from the analysis of observed optical and near-UV spectra are in very good agreement with previous determinations based on different techniques. The silicon abundance is poorly constrained by the UV observations of the continuum and strong lines, but the situation is more favorable for carbon, and the abundances inferred from the UV continuum and optical absorption lines are in good agreement. Some spectral intervals in the UV spectrum of Vega poorly reproduced by the calculations are likely affected by deviations from LTE, but we conclude that our understanding of UV atmospheric opacities is fairly complete for early A-type stars.