My typical game group is 5-12 players for 4e, with 6-8 being average. A lot of socializing goes on and can distract from the game. We let them know it. I whistle loudly and several other players say "Hey lets quiet down and concentrate on the adventure." It works. Sometimes we have to do this a lot, other times not at all. We generate no bad feelings.
For combats, I use to play the grid, which with that many people gets to be a bummer. It would in any system. We do grid less combat. We draw generally where everyone is at. We wing attacks of opportunity, we are generous with flanking, and push/pulls/slides/etc are imagined for effects and may generate opportunity attacks. For area of effects, generally I state as a DM how many I think are in the area as a base, and roll from their. "We will say their are 2 target for it on a 1-3, 4-5 their are 3, and on a 6 4 targets." Works good.
The general thing I like to keep in mind is combats should last no longer than 4-8 rounds. Be generous with players on extra damage.
We do an initiative count. If it reaches your count, and you are not ready with your action and dice, you are passed up until you signal you are ready. Cures players not being ready QUICK. Also If 4 players have a count higher than their opponents, I have them all 4 roll for attacks and actions at the same time to speed it up even more. If they want to cheat, that is their business. Generally players are real good at policing their own cheaters.
I as a DM must keep the flow going and the story moving. If it comes to a rule decision that can be put off for a little bit, I have a player look it up quickly while we continue on. If it needs to be decided right then and nobody really knows how it would work, I make a ruling we can all live with and we move on. We look the rule up later.
Anything I use DM fiat on, I have to make sure the majority of the group is behind it and it makes sense to everyone. We do not argue in game. We save our discussions for after game. What we decide helps us out next session.
Thats my pence worth.