What is wrong with the Aufbau principle that results in so many exceptions?
It's basically because you can't just add up electronic energies using a shell-by-shell, electron-by-electron approach.  As soon as you have two or more electrons in close quarters, they interact with each other in ways that cannot be described by simple electrostatic laws because of the quantum mechanical nature of the electrons.  The comments (specifically Mithoron's) refer to other questions whose answers explain this much better than I can.  Please look at those.