.. snip ..
   if (/^hostname ([-\w]+) /)

or
   if (/^(?:\s+|)hostname ([-\w]+) /)

##</code><code>##

# old line
open F, $path;

# new line IMHO
open(F, "$path") || die "Cant open $path: $!\n";

# or even
open(F, "$path") 
   || ( print "Cant open $path: $!\n" && next);

# another small trim would be to do away with the interim
# array and filename.. 
$filelist = "/var/adm/links/newrun/filelist";

for ( `cat $filelist` ) {
   chomp;
   open(F, "$_") || die "Cant open $_: $!\n";

   while (<F>) {
# anchor could apply here as well.. 
      !/hostname/ ? next : chomp;
 # work on hostname lines here
      last;
   }
   close(F);
   print $hostname. " ";
}