Well you just want to redirect STDERR to some file. The could do this from the shell of course (unless you're running windows, phew), this way :

$./myscript.pl 2>/some/log/file

of course you can manage it from your script :

open ( STDERR , '>>/some/log/file') or 
die "Can't open the log file! : $!";
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The '>>' sign will append errors to the existing file; '>' will overwrite the previous log.