We’ve been seeing the update alert for Android 4.1.2 on our Galaxy S3 for several days now but the update is still queued by request. This morning, we finally got our turn to finally download the update.
Android 4.1.2 fixes some bugs and minor enhancements into Galaxy S3. The update is about 153MB in size.
To update your device, just connect to a local WiFi and go to Settings -> About and hit Update.