Here is the exact error I got. 
(source: clip2net.com)
The favicon.ico has been added in the project as a resource and I have set to ‘Resource’ the Build Action. 
(source: clip2net.com)
I found some solution that require to add some code. My question is why I can’t do it with the Visual Studio Interface?
I had a similar problem with close.bmp. I renamed it to close-image.bmp, and it fixed it. But right now, I tryed to rename it into close.bmp again, and today it works. Seems to be a problem with solution… Read this discussion:
http://social.msdn.microsoft.com/Forums/en-US/vswpfdesigner/thread/b03061e5-5500-442f-9c88-a6d82f97c2b7
Also, your settings are right. You need to include it and make ‘Build Action: Resource’