I think I figured it out.
I typically click once on the item I want to drag and drop, then release, and click again this time trying to move it. I guess I got into this habit from when I needed to drag and drop multiple folders.
With this new track pad, the amount of time allotted between a double click is more (I think) then previous models. So you can click twice with a slightly longer pause between the two and still have it register as a double click.
If I wait just a little longer to click down the 2nd time, the drag and drop works. Likewise, if I just click once, without releasing, and drag & drop, it still works. I can only get it to fail when I almost simulate a double click, but without releasing the 2nd time.