Revealing mistake: Mac and Dillon go after the Predator. The Predator is sitting in a tree, and Mac points him out to Dillon. They both agree that they see it and take position. Mac crawls underneath the alien and is killed by his laser. The Predator then sees Dillon and lasers his arm off. Dillon's arm falls to the ground with the gun firing. Quickly Dillon turns and reaches for the machine gun around his neck. When he turns you clearly see his bloody right stump and his right arm sticking out the bottom of his jacket. [Note: As far as I can work out, this has been cunningly edited out of the UK DVD version].
Revealing mistake: In the scene where Dutch is being chased by the Predator, near the end, he jumps into a waterfall. When you see him take a high-dive, it is archive footage of a different person, filmed on a different camera. When it cuts straight back to Arnie, you can see that it was a completely different place as well. When you know to look for it, this is really obvious.
Trivia: Jesse Ventura was delighted to find out from the wardrobe department that his arms were 1" bigger than Arnold Schwarzenegger's. He suggested to Schwarzenegger that they measure arms, with the winner getting a bottle of champagne. Ventura lost because Schwarzenegger had told the wardrobe department to tell Ventura that his arms were bigger.