Even so, I have discovered lots of new music through Spotify with their recommendations. And that is something Spotify could improve- they need to allow users to directly rate songs (like Pandora does) so it can learn what we like and offer more recommendations. And the other is a better "radio station" type mode, like Pandora has.
Disclaimer: I'm not a Spotify developer, this is just from reading around forums, pissed off at some features not working on Spotify as expected. Here is what I've learnt and it may be inaccurate. Take with salt:
Spotify sort of do the rating mechanic when you click the thumbs up/thumbs down on a song as it is playing (at least on my Android app). "Thumbs up" will add it to a Liked playlist connected to your account.
Now this Liked playlist influences your Discover Weekly playlist. But here is where Spotify becomes retarded. Discover Weekly is not only influenced by your Liked playlist. It's influenced by every song you add to any personal playlist you create but no weight is given to what you actually play(!?). I know right?
My Discover Weekly experience was OK at first, but now it is filled with crap simply because I happen to have a set of "Decades" playlists (the 80s, the 90s, the 00s) just to capture the handful of songs from those eras I liked. So random Top 40 stuff I would never listen to gets shoved down my throat. What really surprises me is that I have playlists dedicated to Dub and Roots Reggae, a well pruned collection of Grunge, Ambient music and Deep House. But none of those ever seem to influence my Discover Weekly experience. Which leads me to believe the so-called "algorithm" for Discover Weekly is there to sell the Top 40 music and doesn't give a toss about your obscure tastes.
What's particularly frustrating is you as the user have no control over this "algorithm" and can't force it to "reset". I ignore it now.
That said, a couple of months ago a new feature was forced upon us (in the UK at least) called Your Daily Mix.
These are supposedly doing the same thing as Discover Weekly but split into 4-6 "genres" and mixing music from your playlists in those genres with new discoveries. Here's to hoping it works as desired.