What most writers tend to do is to try and get everything right the first time. Some gifted folks can do this, yes. But for us normal beings, we have to create a draft first and edit later. There's nothing wrong with that, mind you. And this is especially true when you are literally at a loss for words.
Something I read somewhere: spit it all out and just clean your mess up later.
So here, you edit. If you are not time-constrained, it would be best to do the proofreading a couple of days after you've written the piece. This will allows you to have a fresh perspective. Errors would be easier to catch if you haven't just committed them. If you have a deadline to meet though, editing 2 hours after writing would be okay. You just have to be more vigilant.
TIP: Read your piece out loud. Hearing, instead of just reading with your eyes, will make your mistakes more obvious.
IMPORTANT: The polishing part is NOT to be skipped. If you think you were perfect the first time, you are probably wrong. You may have typos somewhere, or you may have missed typing a word. These are very small mistakes, but it would be embarrassing to have your client think that you did not even bother to proofread.
See, simple right? Again, when in doubt, just "spit it all out and just clean your mess up later".