Just noticed this problem on my phone.  My playlists (imported from iTunes) are complete on Google Music Web interface, but the phone has only partial lists or no songs at all.  Found that while viewing the playlist with my browser  the My Library tab, grabbing and dragging any of the songs titles listed in a playlist, then releasing it, causes a sync to occur with my phone, and when it's done the playlist is complete.  Tried it on 3 incomplete or empty playlists and has worked each time.