Also, make sure you turn calibre off before shutting a machine down so that dropbox can copy calibre's database. Do not shut down the machine until dropbox reports that all files are synced.
While calibre is running, the database is locked, so dropbox can't copy it. Shutting down the machine will kill calibre and break the lock, but also kills dropbox. The copy may or may not have happened. The database stored in the cloud might not be the same as the database on the machine, leading to conflicts, possible data loss, and general confusion.