"Send attachments to" feature would be helpful.
One of the common tasks I find myself performing with Zotero is to use the Show File button for a given attachment to a citation, then copying that attachment to one of no more than a few special folders (including my Kindle's documents/ directory and a USB drive). It would be a nice feature, I think, if there was a specific menu item or button to perform this is one step, much like the "Send to" context menu items under Windows or GNOME's "Copy To" menu item. Eventually, a calibre-like check-in and sync system would be nice for use with e-readers, but a simple Send To like menu would be a great first step, in my opinion.
I certainly would be happy to be able to select a bunch of items, click "email" and have my e-mail client open with pdfs attached and bibliography in the default style in the text body. (even more so, of course, since file dragging has been broken on Linux forever).
But this would seem like something that doesn't need to be super-tightly integrated with Zotero (and might have to be OS specific?)- thus great for 3rd party.