Why would I need a copyeditor?
A fresh perspective can be helpful after you've been over your work again and again. Another pair of eyes can see something you might have overlooked. This step can save you embarrassment or error.
Spell-check won't catch all errors. For example, their and there, passed and past, are all spelled correctly but one will be right for the reader and the other may confuse the reader.
Tiny errors can change meaning and sidetrack the reader. A single comma can be important. There's a big difference between You'll see her, bear with me and You'll see her bear with me.
If errors accumulate in a text, it can cause the reader to lose confidence in the author. A Chronicle of Higher Education story noted how a university press book had to be recalled after readers came across dozens mistakes of spelling and grammar (Howard 2008). A study of researchers, published by the University of Pennsylvania's Wharton School, reported these findings:
[Researchers] make errors when reporting on the papers, either through incorrect referencing or incorrect quotation of the contents of the cited paper.” They go on to cite previous studies of incorrect references in other disciplines ranging from 31 percent in public health journals to as high as 67 percent in obstetrics and gynecology journals and studies of errors in quotation with similarly disturbing numbers, such as 20 percent for medical journals in a systematic survey conducted in 2003. Remember that these errors occur in published articles. The likelihood is that the rates would be significantly higher without the intervention of copyeditors.
Correct grammar, clear use of language, and consistently applied style all put the reader's focus on your meaning--where it belongs.
Howard, Jennifer. 2008. Princeton U. "Press Recalls Typo-Filled Book and Says It Will Reprint." Chronicle of Higher Education (May 2), http://www.chronicle.com/article/Princeton-U-Press-Recalls/40917 (accessed Nov. 29, 2016).
Thatcher, Sanford. 2008. "From the University Presses — The Value Added by Copyediting." Against the Grain 20, no. 4, article 27 (September), http://dx.doi.org/10.7771/2380-176X.5163 (accessed Nov. 29, 2016).