If you were to write the following poem and run it through your spellchecking software, not one word would be highlighted. Every word is legitimate—no spelling errors. Yet you would end up looking either stupid, sloppy, or both. Even if no words are marked by your spellchecker, don’t assume everything is OK. It’s so easy to type “and” when you meant to write “any” or “the” when you meant “them,” these,” or any other common “th” word.
My best advice, which you’ve probably heard from me a zillion times before, is to read what you’ve written out loud (quietly is fine) and slowwwwly: one. word. at. a. time. If you read silently at your usual speed, you’ll end up writing what you think you wrote, not what you actually wrote.