Screen Tearing?

try setting your xbox to 720p instead, if the scaler in your tv is any good it will look just as good (or better in my case),the tv will scale it to 1080p, give it a try for a day or two see if it helps, if the scaler isn't too good it might add input lag or degrade the picture quality.

I will definitely try that.  I didn't know about this method, so I will give it a go with the most problematic games and see if there is any difference.  Thanks!

Unfortunately what it sounds like you are seeing is vsync issues. I know I saw a lot of tearing when I tried Dead Island and Alan Wake employs "smart vsync" when the framerate is over 30fps.

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You can try the recommended setting above but the rendering comes before the scaling and it is also up to the developer to decide if they want the additional cost enabling vsync in their game as having it enable, you take a big hit in performance.

Enabling fixed V-Sync is not always ideal. For an example if you play a game synced to 60Hz and the frame rate drops below 60fps, the game is automatically  re-synced to 30fps. If it drops again (below 30fps), it is re-synced to 15fps and if the same happens again, frames are dropped (meaning it won't be send to the screen). So to provide somewhat stable rate of motion , developers disable V-Sync, which means the majority of frames rendered by the console are send to the screen. But that leads to two different types of problems. 1. Unstable motion and 2, tearing. This is because it's not possible to fit number other than 30 and 15 into 60. So some developers program the game to drop frames while maintaining somewhat stable motion (or repeat the frame 2-3 times). End result: Clean frames but the motion isn't consistent, which is ok for certain games but not for all games. The other option is to merge two frames into one, this leads to tearing (as you're clearly witnessing atm). This provide consistent motion at the cost of visual quality. Certain developers isolate tearing near the top (HALO 3, ODST and Reach all programmed to tear at the top) but not developers have managed to achieve this. If you're playing it on the PC, you can modify the files or force the GPU to enable V-Sync, but on console, there's no such option.