We have surveyed the chemical utility of the near-edge structure of molybdenum X-ray absorption edges from the hard X-ray K-edge at 20,000eV down to the soft X-ray M(4,5)-edges at approximately 230eV. We compared, for each edge, the spectra of two tetrahedral anions, MoO(4)(2-) and MoS(4)(2-). We used three criteria for assessing near-edge structure of each edge: (i) the ratio of the observed chemical shift between MoO(4)(2-) and MoS(4)(2-) and the linewidth, (ii) the chemical information from analysis of the near-edge structure and (iii) the ease of measurement using fluorescence detection. Not surprisingly, the K-edge was by far the easiest to measure, but it contained the least information. The L(2,3)-edges, although harder to measure, had benefits with regard to selection rules and chemical speciation in that they had both a greater chemical shift as well as detailed lineshapes which could be theoretically analyzed in terms of Mo ligand field, symmetry, and covalency. The soft X-ray M(2,3)-edges were perhaps the least useful, in that they were difficult to measure using fluorescence detection and had very similar information content to the corresponding L(2,3)-edges. Interestingly, the soft X-ray, low energy ( approximately 230eV) M(4,5)-edges had greatest potential chemical sensitivity and using our high-resolution superconducting tunnel junction (STJ) fluorescence detector they appear to be straightforward to measure. The spectra were amenable to analysis using both the TT-multiplet approach and FEFF. The results using FEFF indicate that the sharp near-edge peaks arise from 3d-->5p transitions, while the broad edge structure has predominately 3d-->4f character. A proper understanding of the dependence of these soft X-ray spectra on ligand field and site geometry is necessary before a complete assessment of the utility of the Mo M(4,5)-edges can be made. This work includes crystallographic characterization of sodium tetrathiomolybdate.