Hey guys,
I came across this thread this morning after experiencing the same problem as most of you are having, and I believe I've found a solution.
I have a MacBook Air 2012 hooked up to an external LG IPS235. I bought this for design work, and when I connected it via HDMI I found that the color was so bad that was not going to be an option. The monitor was displaying a very washed out effect, in which subtle shades of grey were indistinguishable, or some greys wouldn't even appear on the screen.
I read this thread and decided I'd go out and buy Mini DP>DVI adapter, as the it sounded like this would fix the issue. Hooked the external display up via DVI and found the colors to be better, but only marginally. It was still going to be unusable for my purposes.
I attempted recalibration of the monitor, but still found that I could not get the display looking even close to the standard I require. In despair, I decided to try a different route in calibrating the monitor. I decided to revert the monitor's color settings to default, then Using Mountain Lion's native calibration tool, set it to Expert Mode, then (and this was the most important part) IGNORE THE FIRST SCREEN which prompts the user to "First, set the contrast control to the highest setting" and "Set the brightness control using the image on the right as a guide". After this, calibrate the monitor as per usual following the steps.
The result for me was that this issue was fixed. My display is now producing colors and shades which are good enough to be used for my design work. It's not as nice as the color produced on the Air's display, but that's just because the external monitor isn't as high quality a screen.
Yes, I'm still using the DVI cable, because I couldn't be bothered recalibrating again. But I'm fairly certain this would have fixed the issue with the HDMI cable too, as the DVI cable only marginally improved the colours/contrast.
Hope this helps at least some of you!