We have applied the x-ray extended-range technique (XERT) to measure mass attenuation coefficients over one order of magnitude more accurately than previously reported in the literature. We describe here the application of the XERT to the investigation of a number of systematic effects which has enabled us to ensure that these recent measurements are free from systematic error. In particular we describe our techniques for quantifying the effects of harmonic components in the x-ray beam, scattering and fluorescence from the absorbing sample, the bandwidth of the x-ray beam, and thickness variations across the absorber.