  GALAH+ is a magnitude-limited survey of high resolution stellar spectra
obtained by the HERMES spectrograph at the Australian Astronomical Observatory.
Its third data release provides reduced spectra with new derivations of stellar
parameters and abundances of 30 chemical elements for 584,015 dwarfs and
giants, 88% of them in the Gaia magnitude range 11 < G < 14. Here we use these
improved values of stellar parameters to build a library of observed spectra
which is useful to study variations of individual spectral lines with stellar
parameters. This and other improvements are used to derive radial velocities
with uncertainties which are generally within 0.1 km/s or ~25% smaller than in
the previous release. Median differences in radial velocities measured here and
by the Gaia DR2 or APOGEE DR16 surveys are smaller than 30 m/s, a larger offset
is present only for Gaia measurements of giant stars. We identify 4483 stars
with intrinsically variable velocities and 225 stars for which the velocity
stays constant over >=3 visits spanning more than a year. The combination of
radial velocities from GALAH+ with distances and sky plane motions from Gaia
enables studies of dynamics within streams and clusters. For example, we
estimate that the open cluster M67 has a total mass of ~3300 Msun and its outer
parts seem to be expanding, though astrometry with a larger time-span than
currently available from Gaia eDR3 is needed to judge if the latter result is
real.
