I tried to change the the include/exclude categories using ID as a display method but all I get is a No Categories in the display. Is this a theme issue or just a widget issue?
I want to provide some order to the Categories that are displayed, but this widget does not seem to work.

It sounds like you don't have any posts in the categories and you have hide empty selected in the widget.

Thanks for taking the time to respond. I need to provide more details for you. I want to order the categories in specific ways, but the widget seems to break if I try to change any of its settings in the widget page. It will work with the My Category Order changes for the category order and sub category order, but if I try to use the ID setting and place ID# numbers in the include/exclude tree then I get the No Categories display. If I use the My Order,ID or Slug settings it will work until I put something in the other template boxes.
I realize that this is someones plugin that I am placing in the Widget, and the problem might be theirs, but sometimes there is a theme issue with certain plugins.

The way to determine whether it's a theme issue is to temporarily switch to the TwentyTen theme and test.

I tried that out, thanks for the tip. I found that is doesn't seem to work in Twenty Ten either. So we will move along and if there is an answer to this that I stumble across I will update you.

In the end I built it with html page links and that allowed me to style it in the order that I wanted them to appear.

As is so many things in web work there is often not one simple answer. I'm glad you came up with a solution thus I will mark this thread as solved.