The warnings point to the right direction.

my $request = (
#         POST => $url,
        action => 'Count',
          name => 'datafile',
  Content_Type => 'multipart/form-data',
       Content => [ 'file' => [ $ballot_file ]] );
[download]

You put a list (...) in scalar context, which means that $request will get only the last item of that list.

If mechanize expect an array reference, you have to write [...] around it, if it expects a hash reference it's {...}.