We present a detailed study of the strengths of the calcium triplet absorption lines in the spectra of a large sample of red giant members of the luminous outer Galactic halo globular cluster NGC 5824. The spectra were obtained with the FORS2 and GMOS-S multi-object spectrographs at the VLT and the Gemini-S telescope, respectively. By comparing the line strengths of the NGC 5824 stars with those for red giants in clusters with well established abundances, we conclude that there is an intrinsic abundance dispersion in NGC 5824 characterized by an inter-quartile range in [Fe/H] of 0.10 dex and a total range of ~0.3 dex. As for omega-Cen and M22, the abundance distribution shows a steep rise on the metal-poor side and a shallower decline on the metal-rich side. There is also some indication that the distribution is not unimodal with perhaps 3 distinct abundance groupings present. NGC 5824 has a further unusual characteristic: the outer surface density profile shows no signs of a tidal cutoff. Instead the profile has a power-law distribution with cluster stars detected to a radius exceeding 400 pc. We postulate that NGC 5824 may be the remnant nuclear star cluster of a now disrupted dwarf galaxy accreted during the formation of the Galaxy's halo. We further speculate that the presence of an intrinsic [Fe/H] spread is the characteristic that distinguishes former nuclear star clusters from other globular clusters.