Having spent much time and effort on the content and layout of your CV, it is important to check it. Errors simply give an excuse for a recruiter to put it immediately on the reject pile. You owe it to yourself to avoid that.
Not using a spell checker is inexcusable. It is so easy that not doing so suggests a general lack of care that is not attractive to employers. But a spell check is not enough.
The Sinners’ Bible was printed in 1631 with a lack of proof reading. The word “not” was missed out of one of the Ten Commandments, hence the instruction “Thou shalt commit adultery!”
So proof read your CV, or better still ask someone else to do it. Fresh eyes avoid your brain seeing what it expects to see, when you are reading it for the 27th time.
The same, of course, applies to a cover letter or application form. And the classic mistake if you are addressing it to a named individual is to get their name wrong.