Writing for Content Sites
Most content sites require self-editing. Some do have editors on hand that may make changes. But for the most part, the work you submit should be ready for publication. Many content sites only have people who review your work to determine if it's fit to publish. They don't have time to edit your work, nor will they do so.
They'll just decline it and move on to the next piece. Also, on some of these sites there is the option to self-publish without review. Even though some may allow you to edit afterward, you should always edit before hitting that publish button. This avoids having readers (and potential clients) see those initial typos and errors.
Writing for Private Clients
When writing for private clients, it's pretty much expected by most that your work is ready to use. When someone hires you to write content, they don't want sloppy work. They want something they can just pay for and use right away. That's why they chose to hire a professional. That's you.
By making sure you self-edit everything, you will keep clients happy. Happy clients often return to the same writer and may even recommend that person to friends and business partners. By not proofing and editing your work, you are potentially hurting your writing reputation and career.
Maintaining a Good Writing Reputation
Sure, typos are going to slip through sometimes. But, as a professional writer, you should always do your best work. Even when you know there is an editor, you should submit clean copy that can be published as is. This way, they may not need to correct as many errors. Yes, that means more work for you - in more ways than one.
It may initially be just a little more effort on your part. But in the long run, it can create more opportunity. Also, self-editing is a requirement in some situations, as mentioned above. Writers who are completely or mostly self-sufficient will likely earn more gigs and clients than those whose work requires more tweaking before publishing.
*I originally published a version of this via Yahoo Contributor Network