Try running this:

#!usr/bin/perl
#simpleparse.pl

use strict;
use warnings;

use HTML::SimpleParse;
use Data::Dumper;

my $html = <<'END';
  <div class="views-field views-field-title">        <span class="fiel
+d-content"><a href="/MAKER/gen/id01">Completed 3:46 pm, 06 Dec, 2012<
+/a></span>  </div> 
  <div class="views-field views-field-title">        <span class="fiel
+d-content"><a href="/MAKER/gen/id02">Completed 4:00 pm, 06 Dec, 2012<
+/a></span>  </div> 
END

my $p=HTML::SimpleParse->new($html);
print Dumper($p);
[download]

And see what the data structure from HTML::SimpleParse looks like. It flattens everything out so that it removes all the structure that helps you figure out what you want. You could probably cook up some combination of conditionals to sort out what shows up in what order to get the urls you want, but a fancier module will make your life easier, at the expense of having to read more of the manual.

Here's a solution using HTML::TreeBuilder (which uses HTML::Element for a lot of the interesting stuff)

#!usr/bin/perl
#simpleparse.pl

use strict;
use warnings;

use HTML::TreeBuilder;
use Data::Dumper;

my $html = <<'END';
  <div class="views-field views-field-title">        <span class="fiel
+d-content"><a href="/MAKER/gen/id01">Completed 3:46 pm, 06 Dec, 2012<
+/a></span>  </div> 
  <div class="views-field views-field-title">        <span class="fiel
+d-content"><a href="/MAKER/gen/id02">Completed 4:00 pm, 06 Dec, 2012<
+/a></span>  </div> 
  <div class="views-field views-field-title">        <span class="fiel
+d-content"><a href="/MAKER/gen/id03">Not Completed 3:46 pm, 06 Dec, 2
+012</a></span>  </div> 
  <div class="views-field views-field-title">        <span class="fiel
+d-content"><a href="/MAKER/gen/id04">Something done 4:00 pm, 06 Dec, 
+2012</a></span>  </div> 
END

my $p=HTML::TreeBuilder->new_from_content($html);
my @urls=$p->find('_tag'=>'a');
foreach (@urls){
 if ($_->as_text=~/^Completed/){
   print $_->attr('href')."\n";
 }
}

#print Dumper($p);
[download]

If you want to see how HTML::TreeBuilder parses your HTML into a structure, uncomment the last line with print Dumper($p). Compare that to what HTML::Simple does when it parses. It's a lot more complicated, but TreeBuilder and Element have a lot of methods to make that all mostly transparent.