^ is special symbol. Escape it.

while (<>) {
   if ($_ =~ /\^E/gi || $_ =~ /gmake.*/gi) {
      push (@errors, $_)
   }
}
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which can be simplified to

while (<>) {
   if (/\^E|gmake/i) {
      push(@errors, $_);
   }
}
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It would be more reliable to only check the start of the line:

while (<>) {
   if (/^(?:\^E|gmake)\s*:/) {
      push(@errors, $_);
   }
}
[download]

Relevant doc: perlre