When Parker goes to jail to see Jennie, he wears his pistol into her cell. No police officer would be allowed to take a firearm into a cell.
When Lt. Jamison discovers the bullet in the tree, he removes it by prying it out with a pocketknife blade. Doing this damages the surface of the bullet, which could make the bullet unusable for matching to a particular firearm or to other bullets. The proper way to do it is to cut the section of wood out of the tree and trim it down until the bullet can be removed without damaging the surface of the bullet.