A nonprofit board's duties of loyalty and obedience essentially focus on the concept of faithfullness -- to mission and organization. Behaviors that exhibit failure of faithfullness are not always clear to the eye but include conflicts of interest where personal gain is at stake (kind-of the meaning of conflict of interest) and equally important, speaking without authority (the board's) outside of the board. And yes, there is also the test of whether the board, acting as one voice, has deviated from the organization's mission.
So in the "you will know it if you see it" veign, check-out this conflict going on at the Gay Pride Agenda and chronicled in the Chelsea Now/Gay City News over the firing of the executive. Note, this is not a story about gays and lesbians. This is a story about nonprofit governance and firing an executive director and what happens after.
The question for you: are all board members fulfilling their duty of loyalty and/or obedience?