Although previous direct measurements of the microstructure-fiber continuum have all showed a smooth and stable spectrum, our cross-correlation frequency-resolved optical gating (XFROG) full-intensity-and-phase characterization of the continuum pulse, utilizing sum-frequency-generation with a pre-characterized reference pulse and the angle-dithered-crystal technique, indicates that fine-scale spectral structure exists on a single-shot basis, contrary to previous observations. In particular, deep and fine oscillations are found in the retrieved spectrum, and the retrieved trace contains a "measles" pattern, whereas the measured trace and the independently-measured spectrum are rather smooth. The discrepancy is shown to be the result of unstable single-shot spectral structure. Although the XFROG measurement is not able to directly measure the single-shot fine structure in the trace, the redundancy of information in FROG traces enables the retrieval algorithm to correctly recognize the existence of the spectral fine structure, and restore the structure in the retrieved trace and spectrum. Numerical simulations have supported our hypothesis, and we directly observed the fine spectral structure in single-shot measurements of the continuum spectrum and the structure was seen to be highly unstable, the continuum spectrum appearing smooth only when many shots are averaged. Despite the structure and instability in the continuum spectrum, coherence experiments also reveal that the spectral phase is rather stable, being able to produce well-defined spectral fringes across the entire continuum bandwidth.