Add a META.yml to the distribution. Your buildtool should be able to autogenerate it.
Add a README to the distribution. It should contain a quick description of your module and how to install it.
Split the distribution, or fix the version numbers to make them consistent (use the highest version number to avoid version downgrade).
Add a META.json to the distribution. Your buildtool should be able to autogenerate it.
Define the license if you are using in Build.PL. If you are using MakeMaker (Makefile.PL) you should upgrade to ExtUtils::MakeMaker version 6.31.
Ask the owner of the distribution (the one who released it first, or the one who is designated in x_authority) to give you a (co-)maintainer's permission.
Move your *.pm files in a directory named 'lib'. The directory structure should look like 'lib/Your/Module.pm' for a module named 'Your::Module'. If you need to provide additional files, e.g. for testing, that should not be considered for Kwalitee, then you should look at the 'provides' map in META.yml to limit the files scanned; or use the 'no_index' map to exclude parts of the distribution.
Add 'use warnings' (or its equivalents) to all modules (this will require perl > 5.6), or convince us that your favorite module is well-known enough and people can easily see the modules warn when something bad happens.
Error: CPAN::MakeMaker, WebService::weblogUpdates
This is not a critical issue. Currently mainly informative for the CPANTS authors. It might be removed later.