1. Biological plausibility of back prop.
2. The lack of interest/consideration of time-continuous input on network. They are currently discrete and "learning" and inference is done separately. That's not how most organisms work.
3. The lack of consideration how brains (architecture, not weight) grows.
I might just be me missing something but I really have hard time seeing how things would scale in real world (ex: in Robotics applications of Neural nets) without those things addressed