I thought in the movie, he got the case dismissed by showing that he had changed the firing pin in the rifle so it would not fire.
As for the bullet, if the bad guys had as much influence as they described, they could have substituted the other bullet in the evidence room.
Yes, he showed that he had changed the firing pin, although I don't know how that would keep the rifle from firing. He checked on the paper patching to see if his Dinty Moore bullet might have been used in the assassination (even though a sniper of any caliber would know that a bullet fired through a metal can would be unusable again).
As for substituting bullets, they would have needed a bullet fired from his rifle that would have appeared to have been taken from a body. They had his rifle, and presumably his ammo, so why not get a clean bullet, paper patch it, and shoot the archbishop?
I would think that paper patching would affect accuracy, especially at 1800 yards.