Been having this for some time now (maybe forever? Haven't used Connect much) with different Spotify versions (currently using the latest beta. For some odd reason the forum doesn't let me post version number of the app so I tagged it. The issue is that if I use Spotify Connect to play/control music on my phone then I'm unable to swipe away Spotify's notification when I'm done listening. Even if I close Spotify app on my mac/win10 I'm still unable to swipe away way the notification on my phone. I have to close Spotify from the recent apps menu for the notification to close.
Reinstalls and all that doesn't help. Sounds like a bug to me.