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.
Another reason that the movie almost didn't make its deadline was because the actors kept getting sick. The film was filmed mostly in the Mexican jungle, and aside from dangerous, venomous insects, the actors were often afflicted with high fever, severe stomach ailments, and flu-like illnesses during most of the filming, causing a few of the actors to require several days of bed rest.
Almost all the thermal vision shots were done by artificially colouring negatives shot with a regular camera as the expensive and extremely cumbersome thermal imaging camera couldn't see the difference between the temperature of the actor's bodies and the ambient temperature of the tropical jungle the film was shot in. The few shots which actually use the thermal imaging camera were done by spraying ice water all over the surrounding area and making the actors stand by a fire before filming.
Kevin Peter Hall had to wear a custom made "cool suit" which circulated cold water to keep him cool while wearing the Predator suit in the Jungle. Even with the cool suit he could only wear the Predator suit for about 2 hours before overheating and having to be quickly but carefully extricated from the suit.
When we see the predator polishing and sorting out his skull collection (before the final fight with Arnie), we see some skulls he had already cleaned, and one of them has a hole in the head (where he shot the person we see earlier). Nothing major, but it shows some nice thinking because we only see the skull for a split second.
Only two people were injured during the filming of Predator in spite of all the explosions and gunfire, the first was director John McTiernan who broke his wrist falling from a tree but ignored the injury out of embarassment, the second was the stuntman who did the high dive off the waterfall who threw his knee out when he hit the water.
One of the elements in the sound of the 'snap' to Predator-vision is a whip crack.
Surprisingly, despite the excellent effects and make-up in the film, the budget approval for Predator was so low that within the very last weeks of filming, the movie was almost dropped. Arnold Schwarzenegger also had an obligation he had to keep during the last week of filming, causing him to miss 3 days.