Wrong journal name for PNAS
In Zotero, the 'publication' term of PNAS is always 'Proceedings of the National Academy of Sciences' instead of 'Proceedings of the National Academy of Sciences of the United States of America'. This issue will result in errors when displaying Medline journal abbreviations.
What shows as the publication term in Zotero items is a function of where you saved the data from. All my entries are from PubMed, which has high-quality data. You can also save from the journals' webpages, which tend to have correct data, too. Or use the add by Identifier button.
Any chance you save your papers from Google Scholar? They tend to have missing and incorrect data. If you get your Zotero items from Google Scholar (or other imperfect sources), you may need to correct them in your Zotero library.
If you enter the doi in the Add by Identifier button, the Journal Abbreviation does have U.S.A., but the longer form still doesn't. That's how they seem to have registered their papers.
To fix, you can simply sort all papers in My Library by Publication, and quickly paste in the Publication field the version you want.
I think the right solution here might actually be to fix the abbreviation algorithm to abbreviate ''Proceedings of the National Academy of Sciences' as 'Proc Natl Acad Sci U S A' rather than changing the full journal name. I don't think I have ever seen PNAS cited as 'Proceedings of the National Academy of Sciences of the United States of America' in journals that don't abbreviate journal titles.
For a solution within Zotero, you can do the manual change, or maybe someone more knowledgeable can respond about how Medline abbreviations are implemented.
But generally, you may want to be careful for where you collect bibliographic data: hence, my Pubmed suggestion. It is not that Pubmed has them necessarily more correct than the journal itself. It is, however, more uniform across all biomedical journals.
a) even conceptually, how would you think Zotero should handle that? It could (and maybe should) have a couple more abbreviation lists than Medline, but there's no way it could have journal-level differences for individual style guides like this and
b) does anyeone actually care? I'd assume journals with strong views on this level of detail just handle it during copyedit, don't they? E.g. the New Phytologist explicitly recommends Zotero and we have never gotten a complaint from them.
This is the first line on PNAS' Author's page: "Submit to the Proceedings of the National Academy of Sciences (PNAS) and have your research discovered by millions of researchers in the Biological, Physical, and Social Sciences." Clearly they do not care, as they don't even put it in the metadata they serve on their webpage.
I agree that paying attention to the quality of the data one has in their library is a good thing, and I do modify a thing here and there. But as someone who has published for 20+ years (incl. four in PNAS) and also an editor, I am certain no sane reviewer or editor would or should care about this.
Journal abbreviations is an issue that gets discussed regularly here. More important are probably updates to data, as journals update volume/issue numbers or add DOIs after the electronic versions come out. Or when PMID and PMCIDs are assigned, which you may need for grant applications. I would pay more attention to those issues in your library as you publish. (I think Zotero devs are working to implement an automated data update mechanism, but no ETAs.)