Audio problem: Right after the Jamaicans are massacred in the office tower, a bunch of reporters are all broadcasting from the scene. The camera moves along a row of them. Their mouths aren't in sync with what they are saying. (00:25:50)
Audio problem: When the Predator is about to shoot Gary Busey, just before Danny Glover blows the door in, listen. The actor playing the Predator is counting to three before the explosion, preparing himself for the effect. Easily heard if you turn your tv up. (01:16:15)
Audio problem: In the final scene as the rescue helicopter is landing you can hear its engine spooling down; however the helicopter hasn't landed yet. As the helicopter takes off it does the opposite - you hear the engine spooling up, but the helicopter has already taken off.
Answer: As a reward for besting the Predator in combat, he proved himself a fierce warrior worthy of praise and the gun was a token of their respect for his strength.