Darn, I guess that I spoke too soon.
I now find that what I can see are those which are either my own uploads or previously designated favorites, which have a URL that starts with "http://www.youtube.com/user/......", followed by YouTube userid, followed by the discrete ID of the video. If the URL starts with "http://www.youtube.com/watch?v=", followed by the discrete ID of the video, it does NOT work.
So, a URL like
http://www.youtube.com/user/.. {my userid}.../j
4QN6J4xQ
works (after I sign into the account), but
http://www.youtube.com/watch?v=j4QN6J4xQ {the same video}
does not work.
Is it possible that YouTube changed the coding for the videos, so that Safari and/or Flashplayer cannot negotiate those URLs?
Pete