Spotify integration in Amazing Slow Downer lets you playback songs from all of your existing Spotify playlists and the songs you have in your "Liked Songs" list.
If you miss a song, just switch over to the Spotify player app and add the song to the "Liked Songs" list or one of your playlists.

Spotify audio quality defaults to "Normal" but may be changed to "Low" or "High" in the "Settings" view.

The button top right looking like a circle with an arrow is a "Refresh" button. Tap on this in case of network problems.

You need a "Spotify Premium" subscription, "Spotify Free" is not supported.