Here's a video about what I'm seeing (sorry about volume, keep it low): http://www.youtube.com/watch?v=-CXwV_kwSl0&feature=youtu.be
I haven't tried Campaign yet, but happening on Multiplayer. I've tried two TV's, connection directly to the TV and to my A/V receiver, three different HDMI cables (2 Monster cables), and same thing no matter what.
I do not notice this in any of the CoD menus, Xbox Home menus, only during game play. I see others are reporting similar issues with other games. This won't do it everywhere on the maps, mainly when you are outside of a building, as inside a building I haven't noticed it. Some maps are worse than others, it's very distracting. I would try Battlefield 4 and see what happens, but I can't even get that to load the Campaign or Multiplayer, it moves really, really slow and then will freeze, but I can get to Xbox Home and stuff.
I hope there's a fix or something, but if I have to contact Amazon for a replacement, that's what I'll have to do.