Scary stuff. Haven't run into the error myself (knock on wood) but if I didn't have a PS4 already, I'd hold off on a purchase until this got chased down.
Joystiq reader "Jim" wrote in to report the loss of 30 hours' worth of progress as a result of a glitch that the PS4 console identifies as "Error CE-34878-0." The bug isn't isolated to a specific game, as PlayStation community members report lost progress across several titles in the PlayStation 4's library, including NBA 2K14, Call of Duty: Ghosts, Battlefield 4, and Assassin's Creed 4: Black Flag. In rare cases, "CE-34878-0" prevents users from starting any PlayStation 4 application, rendering the console unusable.