When I'm writing, I'm focused more on plot and character. When editing, I have Chekov's gun and Orwell's directive to never use a long word when a short word will do. I'm looking for every word that ends in -ly and asking it to politely (oops, there's another one) take its leave.
There must be a million and a half blog posts out there like this one, authors extolling the sublime pleasures of killing their darlings, hacking away at the words until the text is lean and ripped as an Olympic swimmer.
I'm currently in round three of line edits on Love Songs of the Revolution. It's amazing how you can find errors to fix or improvements begging to be made on every pass through a manuscript. Every single one!
A friend recently asked me how could I edit my own work. The honest answer is a rather dull one: practice. It also comes from knowing that the editing and even the deleting is the writing just as much as the original task was of putting those first words on virtual paper. The rather more metaphysical answer I'd like to give you is that I'm forever chasing an idealistic vision in my mind of the book I'm trying to write. Perhaps one day I'll get there.