Everyone is so much quicker than me. Oh well, here's my attempt for what it's worth, constructed to handle some (by no means all) HTML-legal variations in the text.

#!/usr/bin/perl -w
use strict;

$/  = '';

my %h;

while (<DATA>){
  while ( s/((\d+) is good.+?)<(?:hr|HR)>//s ){
    my $good  = $1;
    my $key   = $2;
    $good     =~ s/\n?\s?<(?:BR|br).?.?>\n?/|/g;
    my @pot   = split /\|/, $good;
    shift @pot;
    $h{$key}  = [@pot];
  }

}

use Data::Dumper;
print Data::Dumper->Dump([\%h],[qw(*h)]);

__DATA__
<HR>
1 is good<BR>
useless data<BR>useless data<BR>
useless data
<BR>useless data<BR>
<hr>
2 is good<BR>
useless data<br>
useless data<BR>
useless data<br>
useless data<BR>
<hr>
3 is not good <BR>
useless data
  <br />useless data<br />useless data<BR>
useless data<BR>
<HR>
4 is good<BR>
useless data<BR>useless data<BR>
useless data<br>useless data<BR>
<HR>
5 is not good <BR>
useless data<BR>
useless data<BR>
useless data<BR>
useless data<BR>
<HR>
[download]

By the way, you asked your question very well and complete with a good data example. It's appreciated.
(better Data::Dumper, thanks to sacked and tilly).
mkmcconn