“Proofing,” the final step in editing a piece of writing for publication, involves the kind of focused attention that will enable you to find the missing period, the wrong homonym (too instead of to; red when you meant read), or the misspelled word (hell instead of heel) that your spell-checker recognizes as a word and doesn’t correct.
Careful proofreading spares you the embarrassment of announcing in your grant application (as a friend of mine once did) that you “plan a statewide program of pubic education,” or missing a dangling modifier, such as this one in an article on emergency contraception that appeared in yesterday’s Concord Monitor: "To work, a woman must take it within 72 hours..."
One good strategy for getting this important job done right: Ask two sharp readers with a taste for detail to check your work. If possible, pick one who knows a lot about your topic and another who knows little about it. Between them, they'll find the small errors your own eye glides right over.
If you have no choice but to proof your own work, try reading your text out loud and backwards. Reading backwards breaks the neurological feedback loop that gets switched on by familiar sequences of words and meanings, enabling your eye to spot more errors. Reading aloud brings your ears, as well as your eyes, to the task.