1. They can't display black, CRT's can. That's why you have to be carefull with black images, like the one Harry posted.
2. LCD's have a native resolution and changing the resolution to a higher or lower value doesn't always go without problems.
Of course, LCD's do have some advantages, like smaller size and weight, less power usage (I think...?), Deeper colours (That's what people are saying, but I don't see any difference, maybe it's just me though...) and a sharper display (Again, I can't see the difference...).
Also, a lot of people seem to have trouble when calibrating their LCD monitor, judging by the amount of topics about this on forums. Still, it is possible, if using the right tools, like those charts in the links you guys provided. IMHO, a correctly calibrated monitor is the most important thing when you play around with digital pictures.
