When I add the entire map service and enable popups on several layers with that map service, the popups do not work in the resulting web application. When I add just one layer within a map service and enable popups, they do work.
I did mean that when I "click the Browse button and then navigate to your map service in the Browse panel, that the listing of services/the listing of layers within the services are in alphabetical order". I guess as you say this is expected behavior. I wish it was not since it makes things more difficult on my end - finding the layers in the order that I created the map service.