Three problems with backpropagation
Where does the supervision come from?
Most data is unlabelled
The vestibular-ocular reflex is an exception.
How well does the learning time scale?
Its is impossible to learn features for different parts of
an image independently if they all use the same error
signal.
Can neurons implement backpropagation?
Not in the obvious way.
 but getting derivatives from later layers is so important that
evolution may have found a way.