If you find Aperture is hanging, or simply refusing to completely quit when you tell it to, but you’re seeing the dialog “Updating information for sharing previews” on screen (either not progressing, or more likely, seemingly stuck at the end), your sharing database may have become corrupted.

To reset it, open the Aperture preferences, and under the Previews tab, set Share previews with iLife and iWork to Never.

Set “share previews” to Never, then back on, to clear sharing issues

Quit Aperture, relaunch it, and turn it back on, then quit again. It may take a while to quit this first time, as it will be writing the database from scratch, but every subsequent quit should be faster (and, of course, actually complete).

If that doesn’t work, post a question in the forum. There’s a “next level” you can do on this, but it involves opening the package so I don’t want to write that here without discussing the situation first.