Try clearing data from the Play Store. From your Home Screen open the App Drware and then open 'Settings'. Open the 'Applications' section and swipe right to the 'All' tab and then find 'Google Play Store'. Open this up and tap 'Clear data'.
Now reboot your phone, open the Play Store and re login. Afterwards try to install the Spotify app again.
If it still errors do you get an error message? Do you have more the 150Mb free on your system? Can you check there is no Spotify folder at:
/Android/data/com.spotify.mobile
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