The g flag is unnecessary, since you only need to match once. You also don't need two expressions, since you can combine them into one, and if the value is in $_, you don't have to specify it in the expression. The following does essentially the same thing:

while (<DATA>) {
    push @errors, $_ if m/^E|gmake/i;
}

print @errors;

__DATA__
E : abcdfcsds 1387382 43243 

ijigje jg445 3u4 (53545545) 

E : abcdfcsds 1387382 43243 

ijigje jg445 3u4 (53545545) 

E : abcdfcsds 1387382 43243 

ijigje jg445 3u4 (53545545) 

E : abcdfcsds 1387382 43243 

ijigje jg445 3u4 (53545545) 

E : abcdfcsds 1387382 43243 

ijigje jg445 3u4 (53545545) 

gmake : **** build failed fdjgu43uffer Error 1
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Or if you want it to match only when gmake is at the start as well, and just made a typing error:

push @errors, $_ if m/^(?:E|gmake)/i;
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