When Sawyer, Jack and Sayid are swimming towards the boat, you can clearly see that Sawyer loses his gun when he is underwater. However, when he gets on the boat, he has his gun back.
When the sailboat appears in the distance, the bow is facing inland (toward the beach). As Jack, Sayid, and Sawyer swim up and get on the boat, it is still heading that direction. Shots from the boat have it facing out to sea.
When Desmond is dragging the boat onto the beach, he picks up a bottle of wine that is almost full. When he sits down and raises the bottle to his mouth to drink, the bottle is less than half full.
When Jack, Sayid and Sawyer board the Elizabeth, Hume fires several rounds through the hatch. They find him cradling a semi-automatic shotgun, probably 12-gauge, but the holes in the hatch are too small for buckshot and too large for slugs.