A:Answer All sources of TV are generally natively 60hz. TV's that feature 120hz or 240hz fake it, meaning they take a 60hz source and then use it's processors to render it in 120hz or 240hz.
Frame rate is more important. For instance: your Blu Ray movies are at 24 frames per second, HDTV channels in 720p are generally 60fps, and 1080p channels are generally (but not always) 30fps. you would benefit from a 120hz or 240hz TV most if your input source is running higher than 60fps.
A quicker answer is no, you should not be concerned with fast moving scenes in terms of blurriness, artifacting is what you should worry about.