One way to handle this, if the error is consistant, is to use an eval to trap it.

eval {
 open(XMLFILE, '<:encoding(utf16)', $logfile) or die $!;
};
if ($@) {
  # whatever will match your error message,
  # just skip the file.
  next if $@ =~ /^:BOM error/;

  # unexpected message, bail out.
  die $@;
}
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(untested code)

UPDATE: cleaned up the code a little for formatting reasons.