When reporting issues, always mention what version of the Spotify app you're using
Apple now supports users whose devices run older versions of iOS, and thus can't update their apps to the latest version. Engadget has a good article about what it is and how it works. Basically, regardless of your iOS device and version, you can go to Apple's app store and press "update." The app store will then automatically detect the latest, compatible version of that specific app, for your specific device
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This update beings the menu navigation more in-line with iOS 7, but, some might say, it's also become slightly trickier. To get to the main menu from any screen, just swipe right, from the top-left of the screen. have a look:
I like the fact that you have updated the app to take into account the features within iOS7.
There are just a couple of things that I would really like you to consider: The first is that images should play a bigger part than text throughout the app. Have you seen the new Vimeo app, this truley takes advantage of iOS 7?
There is also no Spotlight and News section within the iOS app and I think it would be great to see this included soon.
I always feel that Spotify drip feed updates rather than doing something radical and exciting!