Editing, your favorite thing, right? Actually, I don't mind it, but as I wrote yesterday, I like to do only one thing at a time when I edit. It takes a lot of trips through, but that's good in terms of making the work better.
Readers expect a lot of talking between characters, but that conversation has to do several jobs. For one thing, dialogue reveals character, both the character of the person discussed and the character of the speaker. If Jeannette says, "Robert has always been a bit of a snob," we get a view of Robert and a sense of resentment from Jeanette. If, however, she says, "Robert has always been difficult to understand," we get a less judgmental view of Jeannette as well as a kinder summation of Robert's reserve. The first Jeannette is harsh in her assessment while the second gives Robert the benefit of the doubt.
In editing for dialogue, then, we look for the nuances of language. How does the street bum phrase his description of the killer? How does the socialite phrase the revelation of her husband's infidelity? Syntax and vocabulary must match the characters' education, background, mental state, and motivation. The reader should get an image of a character as much from the way he/she speaks as from any physical description you supply.
Secondly, conversation adds interest to a piece. People speak differently, with different cadences, idioms, and even accents, and the variety livens up the story. Amy Tan's clever use of characters' unfamiliarity with the English language adds both humor and pathos to her work. Yoda's convoluted conversation was a delight, at least in the first movie. Even the terseness of some characters' dialogue sends a message about their inner workings: John Rain and Dark Dexter don't give away much about themselves in conversation. But then, why would they?
Editing for conversational interest involves judging carefully when you have too much or just enough byplay. Some writers try too hard for the partner-patter of successful detective fiction. Such "cute" lines have to be brief and natural, not contrived or belabored, and the black humor that some mystery writers attempt for their cops/coroners/p.i's. can easily become too black, too obscure, or too trite. And don't get me started on those supposedly funny chick-lit women. That can be done well, but mostly it's overdone.
Conversation moves the story along and adds detail. Rather than a paragraph of exposition, a few lines of dialogue can tell what the reader needs to know. Edit looking for places where you can use a character to explain what needs explaining. She can't sound like a college professor lecturing, though. You may need to break it up, have another character ask a question or add a comment.
Sometimes you can't accomplish a goal with dialogue: no character should say, "What a beautiful day with a few wispy clouds skittering across the azure sky." But rather than "It was cold," you might have him say (as many in the Midwest say every day lately), "What a miserable spring! When is it going to warm up?"
Another thing to check out as you edit dialogue is the tags. "He said," "He bellowed," "He sobbed." There is much argument about such things among writers, but I believe that reading once through just looking at dialogue will let the diligent author eliminate a lot of tags altogether and vary those that are necessary. If the speaker is obvious, no tag is needed. If not, a tag can indicate emotion, but tread carefully. It's better for the dialogue itself to convey the mood rather than the tag. A lot of "colorful" tags turn purple, as in purple prose. Certainly adverbs attached to the word "said" must be limited and used only when essential or they smack of Tom Swiftie ( "I'm burning up," she said hotly). If the tag is needed simply so the reader knows who is talking, then "said Bob" works perfectly well.
The final word on dialogue is three words: READ IT ALOUD. Each character should have his/her own sound, major or minor, and whatever they say should sound like a real person said it. Conversational hiccups must be maintained, and any character change that appears in dialogue must be gradual. (Even Eliza Doolittle reverts to her old self under stress.) All dialogue must either advance the plot or reveal character, so as you read, think about whether it does that. That joke you threw in from the Internet won't sound natural unless Robert is in just the right mood. And since Jeannette already told us that Robert is a snob, he probably wouldn't be caught dead telling a joke anyway.