You may already know this, but the "Game Mode" on modern TVs is just turning off the 120Hz/240Hz interpolation that is done to "improve" the picture (or is required for certain 3D systems to work).

The interpolation introduces significant latency that its obvious (and frustrating) during gaming.

I actually run my TV in game mode by default, because the interpolation done in 120/240Hz mode makes everything look like it is slightly unreal and shot on video. Definitely uncanny valley territory.