How to check and correct editorial changes to a manuscript post-acceptance?
I've run into bad editing situations like this. In these cases, I've gone through the paper line by line, with a fine tooth comb. Yes, it is painful, but it is a good idea even if the journal editors aren't obviously screwing up. (This can get doubly horrible if you have complicated formatting in your paper.) You should bear in mind whoever is doing this is unlikely to actually understand what you are writing, and my experience of people doing this sort of thing is that they can be well-meaning and not too bright, so they can take it upon themselves to "correct" your manuscript, while not understanding what they are doing. Additionally, if you give them last minute changes to the paper, make sure to check they have applied them correctly. Are you the sole author? Can you get anyone else to help with this? It would make it less awful.
Your other ideas sound less viable. Asking for a list of changes assumes that there is someone there who actually knows what those changes are. My experience is that journal staff are often amazingly technically incompetent, and probably have never thought of using version control for example. though I'd love to hear about the exceptions. But you can certainly try to insist.
Your passive-aggressive ideas just sound bad. You don't want to withdraw your paper over an issue like that. And if there are errors in the paper, they will reflect badly on you, and nobody else will care.
At times I've thought someone should start a site like ratethisjournal.org where people could discuss their experiences dealing with different journals.
Copy-editing is a normal part of the publication process, and a few errors can be introduced that way. A good proof-reading is in order, of course, but if you miss a typo or two it's not the end of the world. Moreover, if you later come to realize that a critical error has been introduced, which was not present in your initial copy and which you did not find in the your proof-reading, you can always ask for a correction at that point.
However, many publishers give you more information to help review the copy-edited proofs. For example, many publishers will gladly give you (automatically, or upon asking) the list of changes made (“edit track” or something like that). Something a bit like a latexdiff output, in most cases. It's a crowded document, and hard to read through because there are many formatting and copy-editing changes, but it can be helpful with some details.
A Copy Editor speaking. I have couple comments:
It is true that it is impossible to seperate the changes in the text and changes in the formatting, even in good systems like LaTeX.
Good Copy Editor never changes any scientific terms as is. Sometimes we have to change a formula (split in two lines, etc.), or we are dubious about a comma, preposition, hyphen or whatever. Even though the Language Editor corrects these, I sometimes don't make the changes if I feel it is against the intention of the author. Honestly, this is a complicated process, even inside the Editors' Office, not speaking about communication with the authors. As well, we put some notices in the Proofreading version if we're unsure about something, so that the author can be aware of it. Unfortunately, it seems to me that not many journals do quite a great job in Copy Editing.
What can you do:
Read your manuscript really carefully during the proofreading. No matter what happens, you can get as angry as possible at the Editor's, but if there was a mistake in the proofreading version and you did not point it out, it's your mistake, not the journal's.
Prepare the manuscript as perfectly as possible. Use the correct template (esp. in LaTeX), follow the (typo)graphic manual of the journal etc. This way, you minimise the changes the Copy Editor/Typesetter has to make, thus minimising the chance of something going wrong. My experience is that the amount of mistakes that appear is highly dependent of the quality of the manuscript when you send it. (Example: We work in LaTeX, and when I receive an article in Word, I have to re-write/revise all the math formulas. Imagine how many mistakes I make during this very stupid process.)
There are tools that allow a document to be "linearised". Then you can linearise the accepted version and the proofreading version and compare them. However, I don't have any how-to for this.
If you find a serious mistake after the publication, see what errata policy the journal has. In our case, the online version (we're open access) can be corrected, and additionally, Errata are printed in the next suitable issue.