As you can see from the above images there are clearly blue pushpins, green pushpins, black pushpins and white pushpins. There are red pushpins, a few orange pushpins and even fewer yellow pushpins, with a smattering of peach colored pins. It is most probable that they just repainted a number of pins to get the custom coloring they needed. I can tell from another photos on flickr that they did have a number of clear pushpins as well as a freakish variety of skin-toned pins.
If you were going to attempt to reconstruct this on your own I'd recommend you find the cheapest multicolor pushpins that you can (these Universal Rainbow Pushpins are under a dollar) and buy enough to fill your wall. You could save a couple more cents by buying these OIC Pushpins in Bulk if you wanted. Any set of pins will supply you with the basic red, blue, yellow, and green, and finding any specialized colors will be very difficult so you would be better off picking up a can of spray-paint designed for plastic and making sure you get a perfect orange, and a perfect skin tone. Oddly enough Universal does sell a pack of all red pushpins, but any other color you'll have to risk a variety pack.