No one does it anymore, but they should.
Newspapers these days are full of copy errors. I find them in my local paper on a daily basis, usually multiple errors, often in a single story.
100 years ago, a copy error meant correction, sometimes ripping the paper out of the typewriter and starting over again. More recently (like when I was a kid) it meant using correction fluid and correction tape (Do they even MAKE those anymore?). The height of technology was a typewriter that actually had a spool of correction tape built into the machinery. Of course it meant backspacing and retyping over your mistake with the correction tape, then backspacing and retyping the passage correctly.
After that the first word processors (and I'm not talking about software) came into being. They were clunky things. Giant electric typewriters with a one-line display that would let you see what you typed as you typed it, allowing you to make corrections as you went before it actually typed the words on the page. Still, it was basically a typewriter with a delayed response. This machine actually first came out in 1964, but as was par with technological advancements back then it was 10 or 15 years (yes, years, not months) before it became affordable for in-home or personal use. We had an IBM Selectric typewriter when I was in elementary school (the 70s). The Selectric first came out in 1961.
In a way, desktop computer technology came about as a result of the need for more advanced word processing technology. Early word processing machines were basically typewriters with floppy magnetic cards for storing data. The first of these cards could only hold about one page of information. Hardly seems worth it, eh?
The first actual desktop computers--green-eyed monsters that could hold only a miniscule fraction of the information your tiny little iPod can hold--allowed you to type and manipulate a document (all in green lettering on a black screen) before actually printing it, but it still required that you discover and make those corrections for yourself. It wasn't yet smart enough to tell you when you made an error.
According to Wikipedia (which I DO NOT recommend as a primary source of information, but I'll use it here for convenience sake) the first spell check software became available in the late 1970s for mainframe computers. That means those gigantic car-sized computers like you would see in the film Wargames. But it didn't take long for spell-check to appear on personal computers. In the early 80s you could purchase a spellchecker program that ran independent of your word processor program--if your personal computer had enough available memory for it. Many did not. By the mid-80s, WordPerfect and one or two other software companies had incorporated a spell-check into their word processing programs.
Now every word processor, and some online web uses have spell-check capability to check spelling in blog posts, etc. Word processors have gone beyond spell-check with grammar-check.
But they're still not perfect.
FROM and FORM are both correct words. If I type 'I have a package form Gary,' spell-check ignores it. If I type, 'We bought a new more for our horse heard,' spell-check ignores it.
Which is why it is STILL IMPORTANT FOR A HUMAN BEING TO EYEBALL EDIT YOUR MANUSCRIPT!!
Some writers suck at copy-editing. That's OK. Find someone who DOESN'T suck at copy editing to go over your manuscript for you. Ask them to look specifically for copy errors.
But if you're going to try it for yourself, make sure you're up on your grammar. I mean, it's been YEARS for most of us since we had to sit through an English class. Remember diagramming? Do you have any idea what a misplaced modifier is? Do you know the difference between possessive pronouns and pronoun contractions? You should! If you don't know, pick up a style book or a grammar book and study up. The advantage to grammar books for those who really need some brushing up is that they often come with exercises. Do some.
Grammar and spelling mistakes stand out to an editor. If the story has engaged me successfully, I'll overlook one or two copy errors. But copy errors on an opening page are a story KILLER! Manuscripts that are riddled with spelling and copy errors are considered, at least by me, to be WAY not ready for publication.
A) It's common courtesy, B) it makes you look professional.
I'm a busy woman. I don't have time to scour through your manuscript for copy errors before publication. That's YOUR job. If you want to make me happy, if you want your story to have a chance with me--any chance with me--then show me you care enough about my time to do your job.
I had a submission in which the writer said, basically, 'I just wrote this story and thought I'd send it in. Make any corrections you want to.' Um, no. He may as well have said, 'I don't really give a damn about writing. I'm stupid enough to think I'll get rich randomly typing words.' A pro is a pro. He talks the talk and walks the walk. He works hard and does what pros are supposed to do to prove to the world that he is, indeed, a pro. The more YOU make yourself LOOK like a pro, the more respect you'll get, even if your story isn't as good as it could be.
It's all about respect. Respect for me, respect for the business, respect for yourself. Give it and you'll get it.