fault implies a failure, not necessarily culpable, to reach some standard of perfection in disposition, action, or habit.
a writer of many virtues and few faults
failing suggests a minor shortcoming in character.
being late is a failing of mine
frailty implies a general or chronic proneness to yield to temptation.
human frailties
foible applies to a harmless or endearing weakness or idiosyncrasy.
an eccentric's charming foibles
vice can be a general term for any imperfection or weakness, but it often suggests violation of a moral code or the giving of offense to the moral sensibilities of others.