Whenever I finish a first draft of a play, I take a deep breath and may even wander to another project for a while, but sooner or later, I plunge back in. There's an old saying that says something to the effect that most writing is rewriting. It's true.
The first thing I do with my first draft is read through it completely for typographical errors. Sure, there's spell-check, but we all know that spell-check is imperfect: it doesn't pick up words that are misspelled into other words (for example, if you mean to type "hint" but type "tint" instead, it usually takes a human with good editing skills to catch it), and not all programs excel at catching poor grammar.
Usually at the same time I make my proofreading pass, I also make a "tightening" pass. It's still largely mechanical rather than creative, but this time I'm looking for stage directions (the same applies for action in screenplays) that are overwritten. For example, a character doesn't "sit down." He "sits." I make sure that, with the occasional exception, all directions are in the active present tense (e.g. "Mike runs" rather than "Mike is running). The goal is always to describe the action as succinctly as possible.
I make sure that each character gets a proper introduction (age and a phrase of "spin" that allows a producer some sense of that character) and that no two characters have similar sounding names (in practical terms, that usually means avoiding names that begin with the same letter), unless I've made that choice on purpose.
While all of these steps may seem relatively unimportant, they're not. It's so much easier to consider a script's artistic merits if all of the elements surrounding the "art" are clear. For me, once the initial "inspiration" is out of my system and onto the page, each draft, no matter how flawed the content may be, should look absolutely tight and professional.
NEXT UP: The Joys of Rewriting, Pt. 2