I'm a better writer then I was when I joined, but even now with my deluxe new title ("Senior Editor", "Mondo Editor", "Box Hunter") I still have mistakes. It's why we edit.
If you have some reservations about your writing sample reading it out loud tends to help. When you read, say, and hear it you engage your brain more then just reading it. It can also help to let it "age" for a day. If you read it right after you wrote it you're more likely to read what you thought you wrote versus what you actually did.
I've actually used text to speech programs to read things I wrote back to me. The robotic voice hides nothing. The places where flow dies stand out quite plainly, and it's very easy to flip the text and have it reread.
[inter-staff trolling follows]