I am having this exact same issue, I have been trying to fix it for days on end to no avail.
I have a lot of external devices connected to my macbook and I am having multiple different issues but the HDMI to HDMI cable is a fairly standard one for me.
I have the following
rMBP -> HDMI Output -> HDMI Input of a Samsung Syncmaster 2493HM with the latest firmware installed on it, I have the latest version of Moutain Lion installed.
For me, when I boot up my machine with the HDMI connected it will just sit with both screens grey. After going to the apple logo the icon spins a little bit and then just sits at the apple logo with the screen of my external monitor grey. Sometimes I will get 4 squashed spinning beach balls that I can move around with the cursor, I know that the system is responsive cause I always have a curser that I can move around.
I have found that connecting this display to a Mini displayport to DVI adapter makes it work fine every time however this is not an option for me, I didn't buy a Retina Macbook with 2 thunderbolts and a HDMI to not use the HDMI.
I have found that if I boot the machine with the HDMI connected and do a PRAM reset it will boot into the logon screen fine, however if it restart the machine and let it try to boot again I get the same error.
The machine will boot fine with the HDMI connected when it is in safe mode.
If I boot into the recovery partition on my mac, there are no issues with the display.
I installed a fresh copy of mountain lion on an external drive and booting into that and I got the same error with the monitor output.
I attempted to do an install of lion onto an external drive but this mac won't let me because I already have mountain lion.
I used my friends rMBP to test and the same this is happening on his laptop, it booted correctly, maybe twice? but then it was having the same issues.
If I plug the HDMI into my HDMI TV, which is a Samsung something or other, I do not experience the issue.
I have installed windows 7 on my rMBP and it boot fine every time without issues, having said that, windows comes to the logon screen and the lights on my monitor go solid, but the screen remains black until I actually log on.
This is really, really frustrating.
There is a bunch of stuff in the console logs as well but I can't get to that right now because I have just typed this entire thing on windows 7...