We've spent a few hours in Arkham City over the holiday weekend, in between slaving over other review projects and eating sixty pounds of turkey. The game itself is pretty great--if you liked Arkham Asylum, you'll likely love Arkham City--except for one teensy problem that's almost not worth mentioning.
The entire DirectX 11 implementation is broken. And not by a little, either. The game's publishers have acknowledged that "running the game with DX 11 is causing the performance issues," and recommends working around the problem by dropping back to DX9. Note, however, that these aren't just issues--the title is nearly unplayable in DX11.