This is neat! I built a similar service that basically uses song playlist co-occurrence to generate song recommendations for any given Spotify track, and have found some good initial success for more popular tracks / artists [1].
The bottleneck here is using the Spotify API to find relevant playlists - as others have noted here, Spotify's API doesn't provide a way to perform direct lookup of playlists containing a given track, so the best approach I've found is to perform many text-based searches for desired search terms (e.g. artist, song name), and then do breadth-first-search on playlists created by the same users from the initial result set, in order to find other playlists that might have the artist or song you are looking for.
[1] Available in very limited fashion at https://vybe.link; this is a Spotify beta application so the full app only works for whitelisted Spotify accounts
The bottleneck here is using the Spotify API to find relevant playlists - as others have noted here, Spotify's API doesn't provide a way to perform direct lookup of playlists containing a given track, so the best approach I've found is to perform many text-based searches for desired search terms (e.g. artist, song name), and then do breadth-first-search on playlists created by the same users from the initial result set, in order to find other playlists that might have the artist or song you are looking for.
[1] Available in very limited fashion at https://vybe.link; this is a Spotify beta application so the full app only works for whitelisted Spotify accounts