When a weekly playlist (such as throwback thursday or new music friday) is updated, if a desktop application was open before it was changed, and had previously viewed it, they often don't reflect the current (new) contents of the playlist. The only workarounds i've found are if i go into "offline" mode, or restart the application. Most applications which reach out to the internet allow a way to refresh content in case it's become stale.
I'm not sure why these playlists get out of sync (i've had it play the new contents, but refuse to show the new tracks in the UI. I've also used spotify connect and switch to another device which starts playing the previous contents at that playlist entry). This seems like a bug, especially since there are daily playlists that always update accurately.