And in the case we are discussing here, || is very much wrong. Consider the first example of || die in the posted code:

mkdir "$dir", 0777 || die "Could not mkdir \"$dir\": $!\n";
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Here is a demonstration of why this is wrong:

my $dir= "source"; # A directory that I know exists.
warn "Using or...\n";
mkdir "$dir", 0777 or die "Could not mkdir \"$dir\": $!\n";
warn "Using ||...\n";
mkdir "$dir", 0777 || die "Could not mkdir \"$dir\": $!\n";
warn "Done.\n";
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This produces the following output:

E:\etm\Work>perl -w mkdir.pl
Using or...
Could not mkdir "source": File exists
Using ||...
Done.
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Note that -w was silent as well, so I'm not sure when it will warn me of a precedence problem (I'm using Perl 5.6.0).