It seems that the caching scheme used does not properly recognize when the playlist is updated (particularly for automatically generated and updated playlists like Discover Weekly) and a restart of the app is required for the playlist to get updated. A related issue may be present on the iphone because sometimes the old Discover Weekly playlist will remain throughout the entirety of Monday.
That's not cool! Right now, it's not possible to do that. But, you can show your support for this similar idea by voting for it. For now, I recommend doing a quick restart of the app when you need a refresh of a playlist. Let me know if there's anything else.