The new version adds support for the lock screen to allow interacting with music that is playing without having to unlock the gadget to get to the app. It is possible to pause and play the current song, and move to the next/ previous song in the current playlist.
The new app makes a great music service even better. I have long preferred Amazon MP3 for buying music given the good prices and frequent deals that are offered. I like storing my purchases to the Amazon Cloud Drive, giving me access to them from any Android device I use. That's quite a few, considering phones and tablets.
I am already rocking Amazon MP3 on my Nexus S 4G and Galaxy Tab 10.1, both running ICS. The new lock screen controls are extremely useful.
I wish my music collection in the Amazon cloud was directly accessible on the Mac side of things, but there is a work-around for that. When I buy a new album from Amazon I have it configured to go into the Cloud Drive and also download it to my desktop Mac. This lets me easily get it into iTunes on the Mac side, making it available on every device I use.
The new Amazon MP3 app is in the Android Market for easy updating existing installations.