Once the paper is in a shape you're happy with, then it's time to edit seriously.  Editing can be tedious, so it's best to leave time to do it separately.  And it's often easier to make several editing passes through a paper, looking for different things each time.  For example, I usually make one editing pass devoted to style and grammar.  I listen to the sound of my prose, and I pay special attention to the grammatical errors I tend to make most frequently.  Then I do an editing pass devoted to formatting and punctuation.  Are all my citations properly formatted?  Are all my commas correct?  Then, I run my spellchecker.  If your word processor has a spellchecker, and most do, you must get in the habit of using it.  If it doesn't, you need to read through the paper with a dictionary in hand, checking every word about which you're not absolutely certain.

Proofreading

Alas, even if you have a spellchecker, your job is not done.  You must still proofread the paper.  This is necessary for several reasons: a spellchecker can't tell if you've used "there" when you mean "their," won't notice if you've omitted or duplicated or transposed a word, doesn't check for formatting, etc.  You'll find it much easier if you print out a hard copy of the paper to do this.  If at all possible, it also helps to have someone else edit and proofread your paper--another reader is apt to spot things you have missed or passed over.