If you think your piece is done, you're wrong.
The next time you think you've finished an essay, article or blog post, set it aside for a day. If you don't have a day, then wait an hour or two.
Go do something else. Go for a run, go for coffee, have lunch. Get your mind completely off the piece.
When you come back to your text, your fresh eyes will catch typos, poorly phrased sentences and subtle grammatical errors that previously seemed invisible. You'll be more objective about your writing, so you'll come up with better ways to phrase your thoughts more clearly and powerfully.
This is why it's a good idea to finish all writing projects at least a few hours, and preferably a few days, before deadline. The difference between good writing and mediocre writing can be as simple as taking one last thorough look at the text with a pair of fresh eyes.