The problem, which we at Droid Life can independently confirm, is that the playlist shortcut in the sliding menu of the YouTube app has been removed; playlists haven’t actually disappeared, but are no longer easily accessible on mobile. It’s probable that the bug is related to the desktop design refresh Google announced yesterday, but we will have to wait for a comment from the Google or YouTube team before we are certain that’s the case.
Google hasn’t yet acknowledged the bug, but they’ll probably deploy a fix sooner rather than later. For now, you can access your playlists by navigating to the web version of YouTube and starting them from there.
Update: An employee participating in the Google Product Forum thread posted this:
Thanks for reporting this, everyone. Be sure to note if you’re experiencing this on your Apple or Android device (or desktop) when reporting. We’re looking into a fix!Temporarily you can go to m.youtube.com/my_playlists on your mobile device to access your playlists.
Update 2: Playlists appear to be visible again.