I found a PC/AV setting that I had not changed. After setting this to PC, it helped tremendously, but there is still a noticable difference between HDMI and DVI on the the grayscale abilities.
I purchased the P2570 instead of the P2570HD since the performance specs were better, I didn't require a TV tuner, and found it for much cheaper. I connected it to both the DVI input and the HDMI input through a HIS ATI 4670 Graphics card. I was trying to calibrate the monitor and through the DVI input, it looked pretty good. When I switched to the HDMI input I was surprised to see that the picture was very different. The colors were off and I couldn't see nearly the number of differences in grayscale gradients as I did on the DVI input.
Turning MagicColor on (Full or Intelligent) helped the color, but not the grayscale. Why is there any difference between HDMI and DVI?