@seanpatrick, I have been messing with this for a while with the 3.7beta3 version. I had to first go to Products then pick a category from the dropdown (even if you have only one category) and then filter. Then you can drag and drop, and I think there's some AJAX going on there because there is no need to save. It was confusing to me since I only had one category of products, but it makes sense for setting a sort order (can't sort items all at once from multiple categories, at least not in a useful way.)
After you do that, if you view your product page you should see them in the proper order. If you go back to Products, the default view is "all categories" and they will appear in a different order than you previously dragged them to. If you filter again for one category I think you will see the order you set by dragging and dropping.
There is another setting in the Settings > Presentation > "Sort Product By: " drop down, but "order" is not one of the 3 options there. I'm unsure how this fits into the picture right now.