I almost sent off a piece to a client yesterday that had this phrase in it: lunch cancer. It was a piece about...lung cancer. Ouch.
I often hear that copyediting is not needed anymore because of spellcheck and her (mostly annoying) sister, grammarcheck. You can also make an error that turns a word into another word -- just ask anyone who has accidentally arrived to a presentation with the word "pubic" where "public" should be!
But it's really about USAGE, not spelling. If you have an actual word, in the wrong place you won't know it unless you reread the piece. The gold standard is to print it out and read it out loud. If you don't have time for that, ask someone else to read it. Or just read it one more time, even if you don't think you need to -- you'll likely catch at least one small thing.
Here's an example of a perfectly fine paragraph that spellcheck won't catch:
I had two go to the principle's office yesterday, were I saw the affects of what I had bone. Through I had fried my best, I had to except that their where consequences to my factions. Your write to tell me that I'm thorough in this school for ever, but I'm to sad too talk about it at they moment. Its the end of the rode for my career as a spelling teacher.
It doesn't mean don't run the spellcheck tool, it just means spellcheck will not save you. Don't expect it to. Always read your writing twice. Always read your writing twice.