Can any media even output at 240?? I find the 120hz annoying. Looks like it is running at 1.5x speed or something, distracting from the movie.
The TV creates frames that are an 'average' of the frames around it to smooth out the motion. Yeah, the effect is very annoying, makes all movies look like they are B-grade or something. BUT you eventually get used to it and won't notice it until a visitor pops by and whines about it.