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;
};
[download]

while this doesn't:

my $foo = <<'END';
    if ($a == 'bar') {    }
    SELECT foo FROM bar WHERE quz==3;
END
[download]

Are you sure you're not using multi-line quoted strings instead of heredocs...?