This sounds very cool, but I notice there is no mention of expected cost. Another concern is, given this thing will be a half mile in diameter, how susceptible will it be to being struck by meteors, space debris, etc., and how resilient to damage will it be?

This will be a very thin, flimsy "lens", so anything that hits it will leave a hole but pass right through without destroying it. Like a bullet through a target, except 1 KM wide. And very light, probably like aluminum foil.
I just want to know how they're going to steer it, and focus it.

It seems like a drone carrying a telescope might be a better platform than a helicopter to focus on Alpha Centauri.

Being half-mile wide it's going to be affected by tidal forces which will either pull it apart, or cause it to spin (the part closest to Earth will have a faster orbital velocity than the part farther away).

Ok now what about the solar wind in space? At a half mile in diameter that is a huge sail.

What puzzles me is why it is a complete opaque disk. The same edge effect should be there even if it's just a ring.
So why let all that light in the middle go to waste? Reduce the mass by eliminating most of the material on the inside, and combine the Aragoscope with a more conventional telescope.

Isn't this just a giant Fresnel zone plate? http://en.wikipedia.org/wiki/Zone_plate

Any light coming through the center would be unfocused and would interfere with the focused edge light.
These very thin foil sheets (I assume it will be similar to a solar sail) have very low mass should be minimally affected by gravitational forces, by which I suppose you mean the moon.

Great idea. One question: Submarines on Titan... WHAT?

Why not just use the moon as the disc. Being a sphere it will always be in focus-able on wherever one wants by just moving the receiver satellite. It would also be bigger than the 150km disc, and thus be more powerful.