When I plug my Nook into Adobe Digital Editions, I have error messages and some of my books don't show their covers.

While Barnes and Noble eBooks are in the ePub format, they have a special DRM (Digital Rights Management) that most other ePub books do not use. Your Barnes & Noble eBooks cannot be read in Adobe Digital Editions, or on other kinds of eReaders (Sony, Kobo, etc), while your library books can be seen and read in Adobe Digital Editions on your computer.

Don't worry, this doesn't mean anything is wrong with your eBooks from Barnes & Noble, they just aren't compatible with Adobe Digital Editions. However, all versions of ePub, except the Apple iBooks and eBooks, are compatible with your Nook.