I run a group of 6, so I understand the grind fairly well.
Some of the things we've done.
1. DDI Character Builder. Other people have said it, it precomputes everything - this was the biggest help to us.
2. In my group, everyone rolls their own initiative. We have post it notes that run down the side of a white board and one player drives it. Calling out who is next.
3. If someone starts counting squares or doesn't know what they are going to do, 30 second timer gets invoked. If they fail, they delay till the end of the round.
4. As the DM, I try to figure out the monsters ahead of time, sometimes even making myself a list of powers and the order to use them in.
5. Have copies of effects, etc at the table, not in the books.
6. I will often rule on something and then we look it up later. It makes combat much quicker and keeps everyone more involved.
7. The last thing is keeping everyone involved. Once a side conversation starts, it is much harder to keep the flow going. An excellent example of this is our wizard. He's recently retooled to be much more melee based. When he's in melee, totally involved in combat. When he's ranged, yapping away and distracting at least one member of the group.
8. Encourage the tacticians to discuss during someone else's turn, not during their own. That speeds things up a lot as well.