(I know this is an old post but for those interested int he answer, here's one).
You've to differentiate between the wifi driver
(in the linux kernel) and the firmware
(that is uploaded to and runs on the bcm4334 chipset).
WiFi driver cracking is (quite) easily doable.
But there's normally no need to patch the wifi driver: If you're running a standard bcmdhd DRIVER, cracking tools should be run after a LD_PRELOAD
of the fake driver library to make them understand the interface is in monitor mode, without changing the driver.
Now, for the firmware part...
Originally Posted by bcmon team
We are currently working on GS3&4 support (which have a different broadcom chipset), we will release it “when it’s done”.
And that was mid-2013. Bcmon team has not shown any sign of life since (maybe they've been caught by Qualcomm!
So that means, if you want bcmon to work on the Galaxy S3, you've to crack the firmware binary code yourself.
And good luck because cracking steps are superficially documented and human-readable patching source code is non-existent.