How can I make my ice cubes look real?
Two big ones you're missing:


Angle-dependent reflection.  This is one possible cause of your "transparent in places and not in others" effect, and the most likely cause of the missing wetness.
Ice cubes usually have air bubbles trapped inside.  This shows up as a white volumetric haze denser in the center of the cube (for small bubbles) or distinct bubbles (for large ones).  This is the other likely cause of your "transparent in places and not in others".


The techniques for modeling these depend on what rendering method you're using.