Continuity mistake: At the start of the film, Glover's character blows away the Colombians with a shotgun outside their drug den. Immediately afterwards we're shown the Predators POV (in thermal vision) - looking directly down at their bodies, which show up a greenish color. This would indicate their body temperatures dropped to a much lower level impossibly fast. (00:07:00)
Continuity mistake: Shell casings on the rooftop disappear and reappear between shots after Harrigan shoots the drug dealer off the roof at the beginning of the film. (00:10:29)
Character mistake: When Harrigan is watching the surveillance video by Bill Paxton he states that the helicopter is a silver Alouette when it is actually an AS-350.
Revealing mistake: At the slaughterhouse fight, both the Predator and Harrigan shoot simultaneously, Harrigan with the machine gun's grenade launcher and Predator with the gun on his left arm. When the shot is fired, visible on the Predator's weapon is a wire/fuse. (01:17:50)
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.