In AF447, one of the pilots had a nose up input held during a stall. Because the other pilots couldn't see his stick, they weren't aware of his inputs. Also, at certain times, the other pilot was giving contradictory (nose down) inputs to the aircraft. This input was averaged (read: canceled) with the other pilot's nose up input.
The side stick has two problems: 1) Lack of awareness of what inputs are being given to the plane by other pilots in the flight deck. 2) The computer has to make decisions about how to resolve contradictory inputs.