Deliberate mistake: Whenever the Predator is in camouflage, it does not have its signature dreadlocks. This is confirmed in the DVD extras as being too difficult to include them when creating the visual effects.
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.
Continuity mistake: When the Columbians are in the armoury near the beginning, they all look up as a skylight shatters. In the slow motion shots, you can see the leader turn away from the glass. But, then it shows him in a closer shot, and he's still facing the falling glass, and falling back away from it, shielding his face with his hands.
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.
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.