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Device: Galaxy Nexus
Carrier: Verizon
Country / Language: US/English
OS / Browser / build number (if applicable): 4.0.2/?/ICL53F

When I purchased my new phone.  I started using Google Music and I've really enjoyed it. I have one major issue with it though.

My phone/Google Music keeps redownloading offline songs that are already saved on my phone.  Using the data usage monitor feature in the settings menu on my phone, I see that Google Music has used 24.97GB of data over the last 7 days.  Fortunately, I have the "Download via Wi-Fi Only" option enabled in the Google Music settings.  Since, all of this data usage is occurring over wifi on my home network.  Luckily, there are no additional data costs involved.  However, I have a lot of songs inside playlists that I have marked offline and so it takes awhile for all of the songs to get redownloaded.  All the while, my battery on my phone just gets hammered.  If I notice the phone redownloading songs.  I can plug it into the charger.  But some times I don't notice it redownloading all of these songs and in the process lowering the battery level.  I still uncertain on what specific event actually causes Google Music to redownload all of my offline songs. Right now to me, it just seems to occur randomly.  In case it's helpful, I also have the following two options checked in the Google Music settings: "Hide unavailable music" and "Stream via Wi-Fi only." 

Will this be corrected in the 4.0.3 release that will hopefully be released soon.  Thanks.