Plot hole: As the evolved Predator's ship takes off it leaves Casey Bracket alone in hilly forest terrain. The ship then flies a long distance before crashing and the Predator and McKenna start fighting, just for Bracket to show up and help out of nowhere. Impossible for her to cover that distance that fast in hilly forest terrain.
Plot hole: Quinn gave the box containing the Predator's equipment to a Mexican and told him to send it to a P.O. Box in the U.S. He also gave the man an unknown amount of money for the postage. Without questioning IF the Mexican would follow his instructions and had enough money, sending a package internationally is not that simple. The package would need to go through customs and several documents would need to be completed. The contents must be disclosed. It is doubtful it would pass Customs.
Answer: The Predator had landed in the middle of a group of hostile Earth soldiers, who it judged would likely have just shot it immediately. It would have defended itself. And there's also the fact that it could just be for fun because, hey, old habits die hard.