We have used mass spectra from the Vega-1 and Giotto spacecraft's PUMA-1 and PIA impact mass spectrometers to study the Mg, Si, and Fe composition of Comet Halley's dust grains. Automated and manual methods were developed to select only the highest quality mass spectra, rejecting the many spectra with excessive noise, double peaks, data format errors, or molecular contamination. The rigorous selection algorithms accepted a total of 433 compressed (low resolution) PUMA-1 spectra, 29 of the PUMA-1 uncompressed (high resolution) spectra, and 32 of the PIA uncompressed spectra. This selected data set gives results agreeing in general with results of other authors, but differing in some details such as dispersions of ion ratios. Relative to Si, a fairly constant Mg abundance is found, while Fe varies over a very large range. The majority of Mg appears to be contained in silicates, but the wider range for Fe indicates that it is contained in a range of materials such as metal, magnetite, sulfides, and silicates of varying Fe composition. The lack of sharp clustering in the data reveals that (with the exception of some FeS particles) none of the detected particles are single mineral grains. Halley solids are either composed of mineral grains smaller than the typical particle size, or they contain abundant glass. The distribution of Fe/(Fe + Mg) approximately matches the broad, flat distribution of submicron grains in some types of interplanetary dust particles collected in the stratosphere and is quite different from the narrow distribution found in carbonaceous chondrite matrix. The best match is with interplanetary particles that contain high-temperature, Mg-rich silicates and that are dominated by anhydrous minerals. We tentatively suggest that by analogy Halley is a discordant mixture of ice and high-temperature anhydrous minerals. This contrasts with the carbon-rich carbonaceous chondrites that are dominated by hydrous minerals.