If the posterization doesn't show in prints, that should be a big clue that it's the display system at fault. Definitely check into a new monitor, and be aware that any LCD will exhibit a certain amount of posterization unless you get one of the 10-bit Eizo ColorEdge monitors that costs an arm and a leg and a gonad or two. I have a Samsung 213 LCD that does this slightly with certain saturated colors, but it's not visible with most images. CRTs are less susceptible to banding and posterization, but are generally fuzzier and have less brightness and contrast than LCDs.