According to Net::DNS::ZoneFile::Fast:

on_error
An optional parameter, user-defined error handler. If specified, it must be a subroutine reference, which will be called on any error. This subroutine will be passed two parameters: a line number in the zone, where the error occurred, and the error description.

So:

foreach $filename (@files)
{
  $rr = Net::DNS::ZoneFile::Fast::parse(
    file=>$filename,
    on_error => sub {
      my ($ln,$desc) = @_;
      print "Error in $filename on line: $ln\n";
      print "Description: $desc\n\n";
    }
  );
}
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