While the ability to switch to a playlist from the playlist view's top bar, it's not exactly convenient, and the playlist manager is a bit lacking.
There is currently no easy way to view, edit or select playlists.
My suggestion is to add a playlist tab between the Library and YouTube tabs, which, when selected, would display saved playlists in a similar way to the album view. Users could then use the search bar to search for playlists, select playlists, play them, display them in the playlist view, edit them, etc..