  We give two applications of our prior work toward the Putman-Wieland
conjecture. First, we deduce a strengthening of a result of
Markovi\'c-To\v{s}i\'c on virtual mapping class group actions on the homology
of covers. Second, let $g\geq 2$ and let $\Sigma_{g',n'}\to \Sigma_{g, n}$ be a
finite $H$-cover of topological surfaces. We show the virtual action of the
mapping class group of $\Sigma_{g,n+1}$ on an $H$-isotypic component of
$H^1(\Sigma_{g'})$ has non-unitary image.
