  Consistency between cosmological data sets is essential for ongoing and
future cosmological analyses. We first investigate the questions of stability
and applicability of some moment-based inconsistency measures to multiple data
sets. We show that the recently introduced index of inconsistency (IOI) is
numerically stable while it can be applied to multiple data sets. We use an
illustrative construction of constraints as well as an example with real data
sets (i.e. WMAP versus Planck) to show some limitations of the application of
the Karhunen-Loeve decomposition to discordance measures. Second, we perform
various consistency analyzes using IOI between multiple current data sets while
\textit{working with the entire common parameter spaces}. We find current
Large-Scale-Structure (LSS) data sets (Planck CMB lensing, DES
lensing-clustering and SDSS RSD) all to be consistent with one another. This is
found to be not the case for Planck temperature (TT) versus polarization
(TE,EE) data, where moderate inconsistencies are present. Noteworthy, we find a
strong inconsistency between joint LSS probes and Planck with IOI=5.27, and a
moderate tension between DES and Planck with IOI=3.14. Next, using the IOI
metric, we compare the Hubble constant from five independent probes. We confirm
previous strong tensions between local measurement (SH0ES) and Planck as well
as between H0LiCOW and Planck, but also find new strong tensions between SH0ES
measurement and the joint LSS probes with IOI=6.73 (i.e. 3.7-$\sigma$ in 1D) as
well as between joint LSS and combined probes SH0ES+H0LiCOW with IOI=8.59 (i.e.
4.1-$\sigma$ in 1D). Whether due to systematic effects in the data sets or
problems with the underlying model, sources of these old and new tensions need
to be identified and dealt with.
