When you receive a paper proof and review it prior to publication, what exactly should you be looking for?
The things that come to mind are any changes in the annotation of author list and the corresponding author. What else is there?
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This is basically the last chance to fix anything (non-substantial) in the paper, so in addition to the things you mentioned, I usually check for spelling or grammatical errors, misprints in formulas, etc. Sometimes one might want to add a sentence to clarify something.
Finally, if the journal did any copy-editing, you should check its job. Some journals provide a list of changes they made for that purpose. You should also check if the pictures and formulas are still in the right places.
Added: sometimes it's necessary to update the literature list, for example if preprints cited there have been published in the meantime.
One other thing to be concerned about is overzealous copy editors, particularly when it comes to highly mathematical papers. In one of the first manuscripts I ever submitted, the copy editor in question decided that what I wrote as (1/2)x really ought to be 1/(2x). This would have completely altered the intent and the results of the derivation and everything that followed!
So, the lesson of this is that you need to check everything that was changed by the copy editors. If they give you a "mark-up," review that first, and then make sure everything has been transferred correctly to the paper. If not, you'll need to go side-by-side with the submitted manuscript and the final proof, and make sure eveyrhing is as you intended it to be.
I always proofread the full paper, but not necessarily by comparing it word by word with the original. However, I give particular attention to:
Figures and figure captions. In particular:
Equations: most problems I saw introduced during typesetting were in equations. For many publishers, the text is transformed semi-automatically from your original file, but equations are re-keyed by an operator. People make mistakes.
References (citations are a key part of doing research):
Acknowledgment: somehow, I often find that I might have missed someone in the acknowledgment when writing the initial paper, and for most publishers it is not too late to add them :)
For those who can afford Adobe Acrobat, there is a function called compare documents. Here is how I usually proceed.
I generate the PDF of my submitted article. My PDF can even miss several items, like tables and figures (often submitted separateley). Then, I proceed to compare the text of my PDF and the proof. Text-only comparison is an option to be checked when comparing the documents.
The following is a screenshot of what I obtain. It is the proof with some highlighted parts of text. When I move the mouse pointer over the highlighted text, I see what the change was.
In the screenshot, I can see that I wrote psychometrics”1. while they wrote psychometrics”.1, inverting the dot and the 1.
The approach works pretty good with tables.
I know it is not a great answer to tell people to buy an expensive proprietary software. However, it works fine for me. Hopefully there is a free/opensource PDF solution that does the same job.
Between your manuscript being accepted and the proofs being created two things are likely to happen: a copy editor may make changes and portions of the manuscript (e.g., tables) may be retyped (as the manuscript is converted from the format you submitted into the journal format). I know a number of PIs who get two people to look at the proofs. One person reads the proof out loud while the other person compares what was in the submitted version. I know one group that goes sentence-by-sentence backwards. The idea is you never know what will get screwed up in the conversion process. While I like the concept, I spend a lot less time going through the proofs.
One more thing to watch for if the format has changed, say if you submitted the paper in some garden-variety LaTeX style and the journal converted it to its own style: The new line breaks can create hyphenation errors. In general, TeX is amazingly good at getting hyphenation right, but it's not infallible. One of my papers had the misfortune that "colimit" landed on a line break and was hyphenated "col-imit".