Hi Randy,
If you open the web map in ArcGIS Explorer Online (http://www.arcgis.com/explorer/) do the layers display properly? Could you try recreating the web map with maybe just one of the layers and see how that looks? Is the web map something that needs to be locked down/private or is it publicly accessible (where we could take a look)? You might also try downloading a web debugging tool like Fiddler to monitor what is happening when the Application Builder is accessing the web map and services.
Hope that helps,
Katy
Hi Randy,
Apologies, but it looks like possibly a bug. We'll try to investigate further and I'll let you know if we find anything.
Katy