New LCD monitor - black parts of screen "fuzzy"

I recently got an LG 19-inch widescreen monitor with a new system to replace an old laptop.

I've noticed that when the screen is displaying shades of black (but not on total blackness, maybe a dark area in a game cinematic for example), it gets kind of "fuzzy", it's almost like the pixels are jumping around or vibrating, and sometimes there are black horizontal lines moving down those areas. Colours seem fine, but it could just be that it's harder to see these effects with them.

Does adjusting the refresh rate actually do anything with LCD monitors? Does anyone have any other suggestions?

Thanks,
-John07