See:
http://forums.zotero.org/discussion/2909/
http://forums.zotero.org/discussion/3406/

That first thread, 2909, is an unrelated issue: custom ordering of items. Assigning an arbitrary (user-accessible) number to a record hasn't been as widely discussed.

However, along with 3406:

• 1024 suggests using the Call Number field


• 1059 notes that this would probably be addressed if we added support for custom citation keys


• 1149 discusses a few more possibilities, including the possibility that call number functionality might be extended to allow for multiple "locations" (one of which could be your own personal library)
  

And, finally, support for custom item types and custom fields, which would allow this, will likely come eventually. To do that well, though, some exceptionally sticky issues have to be worked out first.

Of course, there's nothing stopping you from manually assigning record numbers using another existing field—ideally one that can be added to the middle pane such as Call Number, Language, or Rights.

Automatic numbering is tricky, though. Zotero itself assigns unique numbers to each item in the database, which theoretically could be displayed to the user—including, quite easily, via a Zotero plugin—but as the Zotero client becomes more and more just a single piece in a more sophisticated larger system, those numbers become less reliable and flexible. This is apparent even with the sync support in the 1.5 Sync Preview: since you can create items on multiple computers and sync them together, you might create items with the same id on each side, and so during the sync process the local id is automatically changed if there's an existing item with the same id in your library on the server. If you already numbered a printed copy and stuck it in a drawer before syncing, that's a problem. These and other issues are part of the reason it's not as straightforward an issue as it might seem.

(The "+" field, by the way, isn't a real field—it's the number of child items an attachment has.)

If your real concern is with being able to generate unique numbers for items, perhaps this site would help: http://www.famkruithof.net/uuid/uuidgen

That site lets you generate UUIDs, or Universally Unique IDentifiers. For more information, see: http://www.famkruithof.net/guid-uuid-info.html

You could generate UUIDs with that site, and then copy them into one of the fields Dan mentioned, such as Call Number, Language, or Rights - any of the fields that can be displayed in the middle pane of Zotero.

I think that would allow you to do the things you say you would like to do, such as sort via record numbers and see record numbers from the list of records without extra clicks. Essentially, the idea is that you would co-opt one of the existing fields (one that you otherwise would not use) to serve as the "record number" field.

There are other ways of generating UUIDs, I just mentioned the online generator since it seems it would be easy to have that sitting open in a Firefox tab, to use while you are adding papers to Zotero.

If you wanted to develop the approach further, you could probably find a way to turn the UUIDs into barcode-type labels to affix to the physical item in one way or another. Then you could use a barcode scanner to scan the UUID into the Zotero search field when you want to locate the Zotero reference for the item. All of that is a bit beyond my own personal level of organization at present, I must admit, but it seems like a system that could work.

I don't know that this helps you with importing your current collection. Maybe if you wanted to move your existing record numbers from the Notes to the field of your choice, maybe it would be possible to do that en masse with a SQLite browser/editor.