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The Galactic All-Sky Survey is a survey of Galactic atomic hydrogen emission in the southern sky observed with the Parkes 64-m Radio Telescope. The first data release (GASS I) concerned survey goals and observing techniques, the second release (GASS II) focused on stray radiation and instrumental corrections. We seek to remove the remaining instrumental effects and present a third data release. We use the HEALPix tessellation concept to grid the data on the sphere. Individual telescope records are compared with averages on the nearest grid position for significant deviations. All averages are also decomposed into Gaussian components with the aim of segregating unacceptable solutions. Improved priors are used for an iterative baseline fitting and cleaning. In the last step we generate 3-D FITS data cubes and examine them for remaining problems. We have removed weak, but systematic baseline offsets with an improved baseline fitting algorithm. We have unraveled correlator failures that cause time dependent oscillations; errors cause stripes in the scanning direction. The remaining problems from radio frequency interference (RFI) are spotted. Classifying the severeness of instrumental errors for each individual telescope record (dump) allows us to exclude bad data from averages. We derive parameters that allow us to discard dumps without compromising the noise of the resulting data products too much. All steps are reiterated several times: in each case, we check the Gaussian parameters for remaining problems and inspect 3-D FITS data cubes visually. We find that in total ~1.5% of the telescope dumps need to be discarded in addition to ~0.5% of the spectral channels that were excluded in GASS II.The new data release facilitates data products with improved quality. A new web interface, compatible with the previous version, is available for download of GASS III FITS cubes and spectra.