How do I clear the 'recently added' playlist?

It isn't set up that way. It is a smart playlist (right click on it to see details) which uses the "date added is last two weeks" command. You would have to change the date added on the tracks it contains to be older than two weeks, or do some other modification to the smart playlist such as only have it display items that had not been played at all. I don't know if there is an easy way to do that unless it is in Dougscripts.

Dougscripts - http://dougscripts.com/itunes/scripts/scriptcount.php?sortBy=Name&op=y - Many itunes scripts

It's obvious now that Recently Added is a smart thingy but it took me weeks to find this thread.

Thanks!