I recently bought a self-published book that had so many editing mistakes, including the heroine's name, that I didn't read beyond page fifteen. I can ignore punctuation or small mistakes but some mistakes were so elementary as to show the author didn't read her own story. She made quite the impression on me. While I will never again buy her books, I wish her well in her career and hope she improves.
Publishing your work is a business. As such, readers expect a certain level of professionalism, which means your work must be as free from common spelling errors as possible.
Working with a publisher.
Publishers use professional editors to improve your story. This is not to say that during the editing process you shouldn't reread your book. You may catch spelling mistakes an editor misses. Most every published book will have a mistake. That is forgivable to a reader. Multiple careless mistakes that take away from a story are not.
Don't rely solely on an editor to catch every mistake. Likely it's been a while since you've read the story when you first get back your edits. Use the opportunity to read, line by line and word by word, what is written. Small mistakes involving the use of he/she are quite common. Spell check doesn't catch these but you can.
Don't be afraid to correct an editor if they aren't understanding your use of a word. Their job is to make your book the best it can be, so work with them so that both parties publish a work that reflects the highest degree of perfection achievable.
Self-publishing your work.
I will state right off that I am not a self-published author. That said, I know many successful authors who are traditionally and self-published. In some ways self-publishing takes more work, time and consideration. You own every mistake in the book you release, without exception.
As I said before, readers will forgive small mistakes, but constant, simplistic mistakes make it harder for the reader and thus they will toss aside your story. You've lost an important person, because they now know you for the wrong reasons, and likely will avoid your books in the future. Let's not forget word of mouth, as well, when it comes to readers.
I recommend using an editing service if you intend to self-publish. Make sure to use one with a good reputation so that you get your money's worth. If you can't afford such a service, use your beta readers.
Lastly, print out your story before publishing. Why? You'd be surprised how many mistakes can be found on a printed version of your book that you wouldn't notice on the computer.
Editing is an essential part of your work and a reflection of your respect for your readers. Don't rush the process just to get your book published. Readers won't thank you for sub-par writing and your reputation is important in this business.
The same care you put into working characters and plot, should also be put into editing. In this sea of tough competition, from the thousands of books released every day, yours can only stand the test of savvy readers through engaging characters and exceptional editing.
Your book will likely contain a mistake or two, noticed once published. Don't stress, it happens to the best of writers. Readers will forgive. Remember though that even bestselling authors are not immune to readers turning their backs for lazy/no editing.
Publish when your work is clean and as error free as possible. It's part of the professionalism of being an author. Take pride and respect your readers.