What I've learned is most proofers are not worth their salt. This will probably trigger a lot of proofers and copy-editors reading this, but most will leave dozens of mistakes behind. And I know they leave that many behind because that's what my beta readers found after getting back a supposedly clean manuscript.
So, I cut out the copy-editing altogether, and until something changes, I'm not going back.
I now use a team of ten sharp-eyed betas. Collectively, they will find far more errors than even the best proofer can. I instruct them to just read the book normally and get back to me within a week. Works like a charm. From time to time after publication, a reader will find an error, but it's no different from before when I used proofers. If anything, quality has gone up.
This is the main problem with most proofers and copy-editors: you will never know if yours is good enough until you've reached a point where thousands of eyes have run across your books. And to be frank, it takes a long time to get to that point, so most writers never learn how bad the proofing in their book is until months, or even years, later. That's enough time for a lot of proofers to get repeat business from the same authors, who eventually drop them a year or two down the road after realizing they aren't getting what they paid for.
The source of the problem is that when you get your edits back, it'll really look like the proofer caught a lot of stuff. As many as 100-200 errors sometimes. But you never see the things they didn't catch. And before you say you should hire at least two proofers, yep, that's what I did. Didn't make much of a difference.
I haven't used a proofer or copy-editor since 2017. Selecting for sharp-eyed betas and having them work in tandem is far more effective and cheaper, and betas are happy to get a first look and save a few bucks on a book. Everyone is happy.
I've found recently that having my book dictated to me through word catches most of the things a decent proofer would catch. My betas hunt up the rest. After using dictations, my betas are actually finding less mistakes than when I used proofers without dictation.
To wind up a long rant, I got tired of spending money on people who leave mistakes behind constantly. I know it's not an easy job by any stretch of the imagination. And maybe my writing is just not clean in itself. As harsh as it sounds, a copy-editor and proofer should be judged by what they leave behind, not what they find. Anything more than 10 errors in an 80,000 word book is simply unacceptable to me and most readers too. At that point, most readers are guaranteed to run across 1-2 errors in their reading, and the grammar fiends even more.
Feel free to disagree with me, but this is simply my experience. An author would do better to acquire a decent beta reading team - easily accomplished by having a page of back matter asking them to report errors to your email. After you get the email, fix the errors and invite them to join your beta reading team.