Curious wrote
Objects lateral to you (the same distance to center), would be accelerating towards you. Assuming it was gravity pulling you, all objects outwards from you, or in front of you, would appear to be receeding, since you would be accelerating faster than anything further out, but any oject closer to center would be accelerating faster than you. So you would be flanked by blue shift, but ahead and behind would be red shifted.
I see your line of thought there, but the fact is that the universe is actually expanding, It's just the accelerating bit that I can't get my head around.
Me thinks we just might about be feeling the G force by now!
My understanding (Which is really limited and will probably get torn up by soem of the others here) is that there is no psuedo acceleration effect because space itself is expanding. Like the expanding ballon anology used elsewhere, as the balloon expands all points on the surface become more distant from each other, but have not accelerated in respect to their particular location in space.
Think of a X,Y,Z graph where the scale keeps increasing, but you keep your same coordinates.