I have created playlists using my Windows Phone 8.1 device. I can see these playlists in the Xbox Music app on my Xbox 360 console. However, only some of them give me the option to play them on the console. The others only show me the option to delete the playlist. These all play fine on my Windows Phone and my Windows 8.1 laptop.
P.S. I've tried to upload screenshots, but inserting media through this interface is a complete fail. I tried to upload .jpg files and it gives me an error saying that I can only upload known file types. Seriously? Never heard of a jpeg?