Running App Version 3.0.5246.30620 on a Verizon Nokia Lumia Icon (929), running Windows 8.0 OS Version 8.0.10521.155.
How to repeat issue:
1) Pin playlist to Home screen.
2) Start playlist from pinned playlist tile.
3) Lock phone after playlist starts, with playlist home screen still displayed.
4) Unlock phone.
Spotify start the playlist over, from the beginning of the first song.
I noticed this issue before pinning songs, so I'm fairly certain this occurs in other usage scenarios. I believe there is an autoplay event which is getting repeated whenever the playlist home screen is refreshed.
Feel free to contact if you'd like additional help troubleshooting/diagnosing.