All you have to do is go to your Likes page and roll over the thumbnail of the site you wish to delete. When the dark screen comes up you will see a white "X" at the top right corner. Press the X and it should be removed. Please let me know if this does not work for you.
Also, if you'd report the URLs that are no longer working, that would be extremely helpful to us in clearly out irrelevant URLs. You can report these here or via the feedback form at http://www.stumbleupon.com/feedback.