Showing Zotero where they are on my hard drive is futile - it never seems to 'learn' where they are.

You can't relocate an attachment outside of the item's directory (e.g., 'storage/BJ2I9XVW') where Zotero puts you (and if it just puts you within the 'storage' directory itself, the expected directory doesn't exist).

But:

Attachment file '/Users/[...]/Library/Application Support/Firefox/Profiles/85iueli4.default-1369740162949/zotero/storage/BJ2I9XVW/[...].pdf' not found

You somehow ended up with an odd Firefox profile directory name (or maybe this is what happens when you reset Firefox)? You can move all the files from the other 'storage' directory into your current one or, if the other profile directory is still within the Firefox Profiles directory (and not, say, on your desktop), use the Firefox profile manager to switch to it (in which case you might want to move zotero.sqlite as well, though assuming the server is up to date it doesn't really matter, since you'll get the latest when you sync).

In either case, make a backup of both directories before proceeding, and I'd recommend disabling auto-sync in the Sync pane of the Zotero preferences before playing with this so that you're sure you have what you expect locally.

All of the pdfs are contained in one directory on my hard drive. With many of them, I drag-dropped into Zotero and then retrieved metadata. With others, I indexed from Google Scholar.

when you drag&drop to Zotero, it places a copy of the file in the zotero/storage folder

Regarding syncing, I don't understand: Does Zotero make two copies of everything? i.e. one in a Storage folder and another on the server?

correct.

I have no current 'Storage' folder (except for one in an old Firefox backup folder).
Can Zotero not just index the hard-drive locations of the PDFs?

not easily, no, and not at all if you want to use Zotero file sync. (more below)

I have no current 'Storage' folder (except for one in an old Firefox backup folder).
Can Zotero not just index the hard-drive locations of the PDFs?

you want to move that storage folder into your current Zotero data folder then.

Either way, why is it still unable to locate files even immediately after I show it where they are?

the error message here isn't great, but Zotero expects those files in its storage directory. It won't accept just any location on your harddisk. (You can use links to files rather than store them in Zotero - that removes your ability to use Zotero file sync—though you can sync files through another means like dropbox—and you need to take some more care for links to work across computers)

it goes into the active Zotero data directory, i.e.
/Users/[...]/Library/Application Support/Firefox/Profiles/85iueli4.default-1369740162949/zotero

where [...] is your username on your Mac.
(see also http://www.zotero.org/support/zotero_data )
note that "storage" should be in lowercase, otherwise you're likely looking at a different storage folder.

The full path of the storage folder would then be
/Users/[...]/Library/Application Support/Firefox/Profiles/85iueli4.default-1369740162949/zotero/storage

And if you get missing file notices after that - e.g. for files not included in your back-up - don't pick a file from your harddisk, but instead delete the file attachment in Zotero and re-attach the file by dragging it to the Zotero item (or by using "attach copy of file" from the paperclip menu)

The crux of the problem is this: Even when I show Zotero where a file is, AND that file is in the Zotero 'storage' folder, it is unable to reattach it.

The folder is Users/[...]/Library/Application Support/Firefox/Profiles/85iueli4.default-1369740162949/zotero/storage

This is a serious bug.

(And if possible open one that you don't mind me sharing the filename for. It will make things clearer.)

Dan - The error is as I mentioned in the original post. I've relogged another attempt for you: Debug D637570657

Right, but I wanted a new one to show you what exactly Zotero is looking for:

Attachment file '/Users/[...]/Library/Application Support/Firefox/Profiles/85iueli4.default-1369740162949/zotero/storage/5FZPT55U/Zunino - A marvellous and useful new world -- Chris Columbus.pdf' not found

So go into the 'storage' directory listed there, making sure you're in that same directory below Profiles. Do you see a "5FZPT55U" folder? If not, or if you do and it's empty, that's the problem. Zotero is only going to look in that directory, because that's the unique identifier of the attachment item you're trying to open. It doesn't matter where else on your hard drive that file might be, and clicking Locate and finding it somewhere else won't work.

So what you need to do is figure out if there's a 5FZPT55U directory elsewhere on your computer — in a backup, say, or a different directory below Profiles, or a previous custom Zotero data directory location — with a PDF in it. Do that first, and then we can take it from there.

That doesn't really make any sense.

If you really think you're looking in the right place, please send two screenshots (Cmd-Shift-4, highlight the relevant section, find the .png created on your desktop) to support@zotero.org with a link to this thread. One screenshot should be from Finder and one should be from the filepicker in Firefox, and they should both show the full hierarchy to the current directory, all the way up to Macintosh HD. I don't remember the specifics in 10.6, but you should be able to do that by clicking on the folder drop-down at the top of the window in Firefox and by ctrl-clicking on the folder icon in the title bar in Finder, or something similar. They should be from either 'storage' or from '5FZPT55U' if it exists.