I have installed and run the leaked version of Android 4.1.2 firmware on my Galaxy S3 GTi9300. From the tested results, this firmware run smooth and almost all basic application and function work stable. If you are interest to update your Rooted Galaxy S3 GTi9300 to this Android 4.1.2 firmware, then you can refer the tutorial here(Link) to update your Galaxy S3 to latest firmware via Odin. But, this is leaked version of Android 4.1.2 firmware for Galaxy s3 and flash any unofficial firmware vi Odin may void the phone warranty. So try it at your own risks.
In my opinion , Samsung will releases official Android 4.1.2 firmware to Galaxy S3 very soon. As estimate, i think that some of Galaxy S3 users will get the official Android 4.1.2 firmware on January 2013. Android 4.1.2 firmware bring lots of new features and application for Samsung Galaxy S3 users. Here is some of features and applications available on the leaked version of Android 4.1.2 (Baseband: I9300XXDLI8, Build Number: JZO54K.I9300XXELK4) for Galaxy s3 GTi9300:
Language:6 languages available
Keyboard input: Samsung Keyboard Input
Call/Receive Cal : Work ok
3G: Work ok
Wifi: CANT Work
Bluetooth: Work ok
Internet Browser: Work ok
Multi Task: Allow user run 2 application on the screen simultaneously. You can enable and disable the Multi Window on the notification Panel.
Camera Best Face Mode : Intelligent Camera Mode that allow you to choose which is the best( face) photo captured.
Paper Artist: Edit photo application
Snap and Go: Snap picture on your computer screen and navigate on Galaxy S3
New Photo Gallery:
Notification Panel: You can customize the notification Panel, Settings>Display>Notification Panel.
Smart Rotation: Smart Screen Display auto adjustment.