Dear N. Harmonik,
What you are getting here is my best guess, based on experience rather than expertise...
A 'flat character' is in the story for the purpose of moving the plot along, and the writer does not develop all his/her nuances. Professor Moriarty comes to mind here, the criminal genius created by Sir Arthur Conan Doyle. Conan Doyle doesn't explore all Moriarty's complexities - we never hear about his deprived childhood or his tragic romance that made him turn evil. And Moriarty never wakes up in the morning with redemption in his heart...
A shallow character (I am guessing) can be fully developed and "round," but is just - well - shallow. Scarlett O'Hara may be an all-time paragon here, Margaret Mitchell's GONE WITH THE WIND...Scarlett's character is explored extensively - her courage, perseverance, resourcefulness...
But at the end she just doesn't 'get' it...as the love of her life is leaving forever (Frankly my dear, I don't give a damn), Scarlett just brushes it all off with "Oh, I will think about that tomorrow..." A fascinating study in shallowness.
