In the first full flashback episode of Lost, we learn a about why Kate was on the plane: she befriended an old man in Australia and he turned her in.  The episode begins with Jack finding Kate's mug shot in the dying Marshal's coat and then transitions to the radio group trusting her with the gun.  Jack is trying his hardest to save the Marshal, but it is a lost cause and the whole beach community knows it.  Sawyer tries to reason with Jack about using up their small supply of medicine, and then with Kate to put the guy out of his misery with the gun.  She ends up handing the gun over to Sawyer, but he messes up and shoots the Marshal's lung instead of his heart.  The other main storyline has to do with Michael promising to find Vincent for Walt.  Michael doesn't trust Locke around his boy, but the older man does find the dog and lets Michael get the glory.