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

symdate();

sub symdate{
my($h,$n,$d,$m,$y,$r);my@x=qw(1001 2002 3003 0110 1111 2112);for('0000
+10'..'195921'){$r=reverse$_;$h=substr($_,0,2);$n=substr($_,2,2);$d=su
+bstr($_,4,2);$m=substr($r,0,2);$y=substr($r,2,4);for(@x){if($_ eq $d.
+$m){if(($h>=0)&&($h<24)&&($n>=0)&&($n<60)){print "$h:$n $d/$m $y\n";}
+}}}
}
[download]

Fixed the logical error and shortened the code down to 179 chars.

sub symdate
{
my($f,$r);for('000000'..'235930'){$f=$_.reverse;$r='(..)'x6;$f=~s/$r/$
+1:$2 $3\/$4 $5$6/g;for(qw(1001 2002 3003 0110 1111 2112)){if((
$_ eq $3.$4)&&($1<24)&&($2<60)){print"$f\n";}}}
}
[download]

Shortened it down to 147 chars though still not as good as chipmunk's. Btw, it generates 8,640 solutions.

sub symdate
{
for(qw(01 10 20 30 11 21)){for$h('00'..'23'){for$m('00'..'59'){$s="$h$
+m$_";$r='(..)'x6;$f=$s.reverse$s;$f=~s/$r/$1:$2 $3\/$4 $5$6/;print$f,
+"\n";}}}
}
[download]

metadoktor

"The doktor is in."