I agree with Corion that you'll need to show the code that produces these issues - I haven't been able to reproduce ProhibitMismatchedOperators at all yet, I've only been able to reproduce ProhibitHardTabs inside q{}'s, not heredocs, and ProhibitImplicitNewlines explicitly states to use heredocs instead of multiline quoted strings.
In other words, this produces ProhibitHardTabs and ProhibitImplicitNewlines policy warnings:
my $foo = q{
if ($a == 'bar') { }
SELECT foo FROM bar WHERE quz==3;
};
while this doesn't:
my $foo = <<'END';
if ($a == 'bar') { }
SELECT foo FROM bar WHERE quz==3;
END
Are you sure you're not using multi-line quoted strings instead of heredocs...?