We report on investigations concerning the shot-to-shot spectral stability properties of a supercontinuum source based on nonlinear processes such as self-phase modulation and optical wave-breaking in a highly concentrated K2ZnCl4K2ZnCl4 double salt solution. The use of a liquid medium offers both damage resistance and high third-order optical nonlinearity. Approximately 40 μJ pulses spanning a spectral range between 390 and 960 nm were produced with 3.8% RMS energy stability, using infrared input pulses of 500±50  fs500±50  fs FWHM durations and 2.42±0.04  mJ2.42±0.04  mJ energies with an RMS stability of 2%. The spectral stability was quantified via acquiring single-shot spectra and studying shot-to-shot variation across a spectral range of 200–1100 nm, as well as by considering spectral correlations. The regional spectral correlation variations were indicative of nonlinear processes leading to sideband generation. Spectral stability and efficiency of energy transfer into the supercontinuum were found to weakly improve with increasing driver pulse energy, suggesting that the nonlinear broadening processes are more stable when driven more strongly, or that self-guiding effects in a filament help to stabilize the supercontinuum generation.