Lots of people have been talking about initiative lately, including (but not limited to) Jeff Rients and Charles Taylor. I basically agree with the idea behind Charles Taylor's approach, although I disagree with his line of reasoning. The key here is to separate which player goes first from which action happens first.
In an RPG, which player speaks first rarely matters. This is why Ron Edwards and the indie RPG people started designing their games with a "free and clear" phrase, where everyone discusses what they're thinking of doing and can change their minds, followed by the actual conflict resolution phase. Their practice resembles what Charles describes, although they take it much farther, in ways not relevant to what we're talking about. Order of player decisions really only matters in games where information about the decisions of opponents can alter your own decisions and give you an advantage. That rarely applies for D&D. The surprise roll provides a tiny taste of this, though, and is probably more than enough to scratch that itch.
In contrast, order of actions can really matter. Take the example that Charles gives, where we supposedly can't tell if "Bill is going first, or Ogre #1, or Wilma, or Phil". Most of the time, perhaps not, but as soon as one of them strikes a killing blow, it matters which goes first, because anyone who is dead doesn't get a turn.There are a couple other cases, not involving death, where when an action occurs matters.
But, as I said, I agree with the general idea. It does not matter which action is resolved first except when it does. So, I think checking Dex order after a killing blow or similar action that reduces an opponent's options is good; for other actions, we can ignore the actual order. I am, however, in favor of rough initiative groups, which I've characterized before as Hasted, Normal, and Slowed (or Overburdened or Fatigued.) Most of the time, everyone will be in the Normal group, and actions can be considered to happen simultaneous, except as noted above. But in a fight with zombies, I make the zombies go last... and I make the exhausted characters go last, too.