If you use an array of hashes, the sorting becomes quite intuitive:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];

my @data;
while( <DATA> ) {
    my( $col, $cnt, $stat, $miss, $mod ) = m[
        ^
        Collection=>(\d+) \s+
        ImageCount=>(\d+) \s+
        Status=>(\w+ ) \s+
        Missing=>( [1-9,]+ )? \s+
        Modified=>( .+ )
        $
    ]x or warn "Bad format at line $.\n" and next;

    my( $day, $mon, $year, $hrs, $min, $sec ) = 
        $mod =~ m[(\d+)/(\d+)/(\d+) (\d+):(\d+):(\d+)]
        or warn "Bad date format in line $." and next;

    push @data, {
        Collection => $col,
        ImageCount => $cnt,
        Status => $stat,
        Missing => [ split ',', $miss||'' ],
        Modified => sprintf( "%4d/%02d/%02d %02d:%02d:%02d",
            $year, $mon, $day, $hrs, $min, $sec ),
    };
}

##pp 'original order',  \@data;

## Sort data by image count descending and modified date ascending
my @ordered = sort {
    $data[ $b ]{ ImageCount } <=> $data[ $a ]{ ImageCount }
    ||
    $data[ $a ]{ Modified } cmp $data[ $b ]{ Modified }
} 0 .. $#data;

print  'Sorted by Image count descending and modified date ascending';
pp $data[ $_ ] for @ordered;

__DATA__
Collection=>168245 ImageCount=>6 Status=>SI Missing=>1,3 Modified=>01/
+18/2012 11:14:30
Collection=>161745 ImageCount=>6 Status=>I Missing=>2,3 Modified=>01/1
+8/2012 11:16:38
Collection=>162451 ImageCount=>6 Status=>SC Missing=> Modified=>01/20/
+2012 11:16:38
Collection=>117481 ImageCount=>8 Status=>C Missing=> Modified=>01/18/2
+011 7:16:38
[download]

Produces:

C:\test>junk53
Sorted by Image count descending and modified date ascending
{
  Collection => 117481,
  ImageCount => 8,
  Missing    => [],
  Modified   => "2011/18/01 07:16:38",
  Status     => "C",
}

{
  Collection => 168245,
  ImageCount => 6,
  Missing    => [1, 3],
  Modified   => "2012/18/01 11:14:30",
  Status     => "SI",
}

{
  Collection => 161745,
  ImageCount => 6,
  Missing    => [2, 3],
  Modified   => "2012/18/01 11:16:38",
  Status     => "I",
}

{
  Collection => 162451,
  ImageCount => 6,
  Missing    => [],
  Modified   => "2012/20/01 11:16:38",
  Status     => "SC",
}
[download]