I definitely edit in waves. One thing I do, once I have a complete draft, is track a single character from beginning to end. I make sure that character is vivid, that he has a clear story arc, a definable desire that’s always with him, no matter who or what he faces. I do this for every single character, no matter how small his role in the story. And I also do this for the setting, which I consider one more living creature in my story.
I tend to focus on the central character of a story. I read and revise with that character's arc and desires in mind. In my single-mindedness, I probably neglect secondary characters (sometimes even to the degree that I treat them as props, or worse--as obstacles shaping the central character's journey). I hope this isn't always the case, but Susan Henderson's suggestion to read through a story with an eye for the vividness and plausibility of secondary characters strikes me as a good idea.
Come to think of it, I may have done just that in my most recent published story, "From the Canyon to the Driveway." Granted, the woman in the opening paragraph doesn't take much of a journey--but the father does. That is, until he doesn't.