[ This is my new answer to the new (i.e. updated) question. ]

Style issues aside, there's nothing wrong with your code. It works for me with no changes. For example,

while (<DATA>) {
   if ($_ =~ /^E/gi || $_ =~ /gmake.*/gi) {
      push (@errors, $_)
   }
}

print(@errors);

__DATA__
E : abcdfcsds 1387382 43243
ijigje jg445 3u4 (53545545)
E : abcdfcsds 1387382 43243
...
E : abcdfcsds 1387382 43243
ijigje jg445 3u4 (53545545)
gmake : **** build failed fdjgu43uffer Error 1
[download]

outputs

E : abcdfcsds 1387382 43243
E : abcdfcsds 1387382 43243
E : abcdfcsds 1387382 43243
gmake : **** build failed fdjgu43uffer Error 1
[download]

Are you saying you are getting something different?

I said "style issues aside" earlier, because your code stands to be improved. $_ =~ is unnecessary, /i is unnecessary here, /g is even more useless, and your regexps would be more robust if they were more restrictive, as follows:

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