Your source of error has been identified by others, ie., the token parser is not scoped/recursive, and your inner loop looking for options caused side effect on the outer loop, which exited prematurely.

Being the HTML Token Parser, it's good at parsing tokens. :-) You could rewrite your loop using the token parser, instead of the get_tag.

...
while (my $token = $parser->get_token)
{
  next unless $token->[1] =~ /(?:select|input|textarea)/;
  if ($token->[0] eq 'S') # start tag
  {
    $count++;
    my $tag   = $token->[1];
    my $name  = $token->[2]{name}; # fetch name of input
    my $value = $token->[2]{value};
    my $maxlength = $token->[2]{maxlength};
    my $required  = $token->[2]{required};
    my $allowed;
    if ($tag eq 'select')
    {
      while (my $option = $parser->get_token)
      {
        last if $option->[0] eq 'E' && $option->[1] eq 'select';
        next unless $option->[0] eq 'S' && $option->[1] eq 'option';
        push @{$allowed}, $option->[2]{value};
      }
    } else {
      $allowed = [ $token->[2]{allowed} ];
    }

    $DEBUG && print "$count\t$tag\t$name\t\n";
    if ($tag eq 'select') {
      print Dumper($allowed);
    }
  }
  ...
}
[download]

And the debug output shows:

1       input   text1
2       textarea        textarea1
3       input   radio1
4       input   radio1
5       input   check1
6       input   check1
7       select  list1
$VAR1 = [
          '1',
          '2',
          '3'
        ];
8       input   text2
[download]