Saved items not in Library
I tried saving several items through the JSTOR database using Safari and a pop-up said that it saved the item. However, when I went into my Zotero, none of those items appeared in my library.
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Upgrade Storage
Do you remember in the "Saving" bubble - where the titles of the items listed? If so, they were almost certainly saved somewhere.
Edit: also, please provide a Debug ID from Zotero Standalone for an attempt to save an item.
And you don't have anything odd with your setup, like Zotero Standalone and Zotero for Firefox in server mode or MLZ in Firefox running at the same time? (if you don't know what that means, then you probably don't)