I've been having the problems with my S3 not being seen in Windows as a USB drive but I think I found a very simple solution to the issue. Also if you use Media Monkey this will also help the program see the device and sync it with playlist and what not.
1. Install the latest Samsung drivers found from the website. (Using the Verizon program is not necessary)
2. Plug your phone into the computer. If your computer does not see the device in the My Computer screen you have the wrong drivers make sure that at this stage your computer at least sees that you have a media device plugged in.
3. When your computer sees the device and installs what it needs to open your phone to the main screen there you should be able to see a USB icon on the top left hand corner where your messages.
4. Swipe the menu down as if you are looking at your messages then tap on the box that will say "Connected as a media device"
5. You should now have two options the first being a multimedia device (MTP) the second should be Camera (PTP). While your device is still plugged in switch it to PTP. At this point your computer should now see your phone as a camera and you should be able to open it and see the files and folders located on your phone.
6. Now with seeing the file directories on your phone switch it back to MTP on the phone and you should get the same view of the directory but now with your computer seen as a media device not as a camera.
7. You know when it's successful when a Windows Media Player window ask you to sync your device.
8. (Optional) If you are using Media Monkey and your computer can now see the media device Media Monkey should see it as well without a restart of the program or any additional software. But you should have the latest version of Media Monkey just to be on the safe side.
If this works pass it on as Verizon is the worst with Tech Support believe me. This is also why I have the Galaxy S3 vs. the Droid ULTRA
For those who would like to know I found this fix on a computer running Vista Home Basic with the latest updates and Service Pack 2 so anything above that should work.
Note: For some reason the S3 does not support FLAC audio files so you will have to convert to a different format to add them.