I'm experiencing the same problems as well. I'm running a GTX 970 and when I use DirectX11 with max settings I get all kinds of graphical glitches that make the game literally unplayable.
Putting the settings down to high does remove some of the glitches but it gets worse over time. Especially complete character models that just start to disappear, totally ruining the immersion. The only way I can properly run the game is to put it on DirectX9 but that sets all the options back to medium. It feels wrong not to be able to play a game such as this when your hardware can easily handle it, especially in this day and age.
I really hope EA, Bioware or Nvidia for that matter fix these issues. I've played and completed the original Dragon Age Origins plenty of times without much problems, it would be great to be able to properly play Dragon Age 2 before moving on to Dragon Age Inquisition.