I bet the doppler shift from two different listening microphones would give you a pretty easily calculation for how fast the gun was moving (at least relative towards/away speeds with respect to the two microphones) - I'd guess 3 or more microphones listening to the same gunshot could pinpoint both direction and speed.
I was thinking about the Doppler too, but the Doppler shift of the bullet while in flight doesn't really do it. And the time-frame to do it while inside gun is really really small.
