  Astrophysical tests of the stability of fundamental couplings are becoming an
increasingly important probe of new physics. Motivated by the recent
availability of new and stronger constraints we update previous works testing
the consistency of measurements of the fine-structure constant $\alpha$ and the
proton-to-electron mass ratio $\mu=m_p/m_e$ (mostly obtained in the
optical/ultraviolet) with combined measurements of $\alpha$, $\mu$ and the
proton gyromagnetic ratio $g_p$ (mostly in the radio band). We carry out a
global analysis of all available data, including the 293 archival measurements
of {\it Webb et al.} and 66 more recent dedicated measurements, and
constraining both time and spatial variations. While nominally the full
datasets show a slight statistical preference for variations of $\alpha$ and
$\mu$ (at up to two standard deviations), we also find several inconsistencies
between different sub-sets, likely due to hidden systematics and implying that
these statistical preferences need to be taken with caution. The statistical
evidence for a spatial dipole in the values of $\alpha$ is found at the 2.3
sigma level. Forthcoming studies with facilities such as ALMA and ESPRESSO
should clarify these issues.
