When Mathews and Williams get into the helicopter, the large rope is not in the helicopter. It appears when Williams returns to the helicopter after leaving the cave.
When giving Mathews the stolen vehicle location, the dispatcher is clearly reading his lines.
Mathews calls for the helicopter to meet him at his location and then gets in his car and leaves.
Williams does not tie a knot in the rope after he attaches it to the helicopter.
Mathews tells Williams this is the first time he's been shot at with his own gun. Mathews carries a snub nose (short barrel) revolver. The criminal used Williams' long barrel revolver to fire at Mathews.