My half-assed try... 67

for('00'..'99'){$a.=$_ unless $x{$_} or $x{reverse $_}++};print $a;
#234567890#234567890#234567890#234567890#234567890#234567890#234567
#        1         2         3         4         5         6
[download]

Note, it includes '00' which some people are missing...

Update... 59? (similar to hardburn's solution)

for('00'..'99'){$x{$_}++unless $x{reverse()}};print keys%x;
[download]

Update 2 ...50?

for$a(0..9){for(0..9){$x.="$a$_"if$_>=$a}}print$x; [download]

Update 3: after a clarification, i guess i've misunderstood the problem. I thought it needed all unique pairs, separately (ie. 00, 01, 02, 03...). My bad.

Update 4: Here's one that actually passes the checker (60)

$_=9;for$a(0..9){for$b($a..9){$_.="$a$b"}s/$a{3}/$a$a/}print
[download]

Update... 57!

$_=9;for$a(0..9){for$b($a..9){$_.="$a$b"}s/$a$a/$a/}print
[download]

--
"To err is human, but to really foul things up you need a computer." --Paul Ehrlich