Meaning of the opening shot (the glass and ice)
The opening shot of Miller's Crossing features an empty glass with 3 other glasses behind it, and 3 colourful flasks to the right. Tom drops ice into the glass one, two, three, and then pours whiskey over top of the ice, and gives it a swirl.
I get the impression from that shot, and the scene, that the ice cubes represent Leo, Caspar, and Eddie Dane, all getting mixed in together with Tom holding the glass and in control.