Question: I am trying to make an original character who is blind
and hunts with bow and arrow from a flying mount. 
(Obviously, no existing animal can fly while bearing the weight of a human,
so let’s assume that the mount is a mythical/fantastical species;
for instance, a dragon or a gryphon.)

What physical qualities (internal/external)
would enable and enhance the archer’s feasibility and hunting prowess?

Answer: 
This is somewhat generic
(i.e., it goes to support the feasibility of a blind rider
controlling a flying beast, and not so much the archery aspect),
but, since telepathy has already been mentioned:
a psychic link between the rider and the steed would be very useful. 
Even if it doesn’t go so far as to allow
the rider to see through the mount’s eyes (as [suggested by James](https://worldbuilding.stackexchange.com/questions/45212/#comment127266_45257)),
it would be very handy if the mount could alert the rider
to upcoming maneuvers, or if the rider could direct the mount,
all without making a sound. 
Compare to the [neural interface](http://www.avatarmovie.com/index.html) between creatures
(including the bond between rider and steed) in James Cameron’s [*Avatar*](https://en.wikipedia.org/wiki/Avatar_(2009_film)).

Also, you might want to look at the [Nazgûl](https://en.wikipedia.org/wiki/Nazg%C3%BBl)
(from *The Lord of the Rings*) for some general inspiration. 
While they are not totally blind,
they [do not see the world of light as we do](https://scifi.stackexchange.com/q/14876/30482#14880 "Lord of the Rings – Are the Nazgûl Blind? – Science Fiction & Fantasy Stack Exchange"). 
(They may use a sense of smell when on the ground;
it’s not clear whether that would be useful when they are airborne.)
How about ability to see/detect minute alterations of Earth's magnetic field or electricity? That might allow him to detect live beigns from a distance. I assume a medieval background due to the presence of mythical creatures so no radiowaves everywhere to drive him crazy, though his perception of a thunderstorm would be interesting.

Can't imagine the kind of organ which would allow, I can only think it would have to be duplicated to allow triangulation for distances. Maybe replacing the eyes?