[Sirtel]

It can be done (i.e. keep your library in Dropbox and access it from two computers), but you must be very-very careful, as Calibre doesn't really support it. The right way to do it is to pause Dropbox, open Calibre, make changes, close Calibre, resume syncing, and when the syncing is done, quit Dropbox. Then the same process in the same order on the other computer. Never run Dropbox while Calibre is open, and don't leave Dropbox syncing on the background.

Also you should run Library Maintenance regularly, as errors still happen, no matter how careful you are.