I have rooted 3 other GS3's using the method listed here:
All other roots worked great! I was able to flash TWRP (I realize that the specific tutorial above calls for CWM instead of TWRP) and then install a CyanogenMod ROM. However, this time it did not go well.
I forgot to enable USB debugging before flashing VRALEC the first time, and when I went to run TWRP (2.7.0 for d2vzw) I realized that it did not mount the file system I thought that this was unusual and then realized that I need to enable USB debugging. I completely unrooted the phone and installed stock recovery and rom (VRBMF1, Android 4.1.2) once this was done I figured that I would go back to a personally tried and true version of TWRP (2.5.0 for d2vzw). At this point I was careful to ensure that I enabled USB debugging before proceeding with the root process.
With TWRP 2.5.0 I was prompted with a password. This befuddled me and upon some reading on the forums I came across a solution that worked for others but NOT ME. (Essentially you clear the cache and to a factory reset 3x in TWRP recovery and it will stop prompting you for the password and mount your file system correctly). For me I was unable to mount the cache for dalvic-cache to wipe it and factory reset does nothing.
I have rooted and unrooted my phone approx seven times trying different versions of TWRP, CWM, and even trying to use a seperately downloaded VRALEC file just in case if mine had an error.
I also came across this thread (below) and it did look somewhat promising however it is for android 4.2.1 and I don't want to mess up my phone any more than it already was. I am getting similar (not exactly the same) errors in my TWRP. I also made sure to use the same bootloader that I used on other 4.1.2 android systems in addition to using the d2vzw version of TWRP (It is for this reason that I am not sure that flumpster's comment applies to me). I figured that I would include this information just in case it was helpful:
Any Ideas? I am really looking forward to trying Liquid Smooth 3.0!