I'd say go for a different colored tick, say red instead of green for a problem book.
IIRC in the library view i.e. in the on device column, there is already text indicating where the book is, that text can be special cased for this as well.
In the device view, i.e. the in_library column we can add text as well for problem books.
Sorting: problem books should sort first, then non problem books then not on device books.
Search: Not sure about that one, given the sorting above, I dont think its particularly important. Given that there is text, i'd say allow searching for that, but, the devil is in the details.
As for the attribute, I suggest
_device_book_problem = "A long message from the driver indicating the problem" or None if there is no problem.
The long message can be used as a tooltip in the GUI, the short indicator text in the column can be a standard string, rather than coming from the driver.
I wont be able to get to this until about two weeks from now, so if you want to do it before then, go ahead.