When Isabelle shows Royce the weird magnetism by using a leaf in water, she puts the leaf on the water and it is very flat. After the cut and close-up of the leaf it is very curled up and cup like. It is very obvious that it is not the same leaf.
When Royce runs to save Isabelle from the pit trap, he throws his shotgun to the side and dives the last several feet, which would put the gun behind him and out of reach. When he pulls her out of the pit, the shotgun is right beside him on the ground.
At the very beginning when Royce is talking to Nikolai for the first time, after the camera pans away, what appears to be a pacing counter on Nikolai's left shoulder disappears in the next shot and then reappears the shot after.
Right at the start of the film, Royce drops through the forest canopy after detaching from his parachute, however the next overhead shot shows his parachute lying a few feet away on the ground - this seems unlikely as the parachute would have tangled in the branches above.
When we first see Nikolai open up with his minigun, the barrels don't appear to be moving. However, this is because of a common stroboscopic optical illusion known as the wagon-wheel effect (caused by temporal aliasing. The best known example of this is when the wheels of a stagecoach appear to be stationary when in fact they are rotating, because they are rotating at exactly the same speed as the camera shutter, i.e. 24 times a second.)
After two of the characters are fighting, one says that they should rescue the doctor who is hanging upside down in a tree. He is hanging nearby screaming continuously, but you only hear him when he is on screen. Nothing indicates that he was within a few feet of them. He was obviously a fair distance away as Edwin was shouting for help and says "thank god" when he sees the other members of the group, as if he was relieved to see other people.
The goof items below may give away important plot points.
When the final predator is killed by Royce, you clearly see its head fall backwards and the body slump forwards. However when the camera pans out showing the scene, the predators head is now in front of is former body at Royce's feet.
Shortly after escaping from Noland's hideout, Stans stabs Berserker Predator in the upper right shoulder with the wound clearly visible from the front. However, once Berserker captures Isabelle and Edwin the wound has disappeared and remains missing later during the fight with Royce.
In the beginning of the movie Royce observes that the sun "hasn't moved", but then later it is nighttime. This is not a goof. Several scenarios are plausible, such as a very slow planetary rotation or an eclipse by one of the system's many nearby planets.
When Edwin is upside down at the beginning of the movie he is asked if he has anything to cut himself down with. He says no, but then pulls out a surgical knife to stick in a poison flower. However, he is a pathological liar as proved numerous times throughout the film. Also, after waking up falling from the sky when he claims he was just on his way to work, he may not have realized he had the kit on him at the time.
When Edwin identifies the plant that Nikolai is about to touch, since they are not on Earth he would have no way of being able to recognize it. The only way would have been for the Predators to have filled the planet with terrestrial flora and there is no reason given in the film for them to have gone to that trouble. As said by Robert Rodriguez in interviews and stated in the FAQ, the Predators took plant-life from all over the galaxy and including Earth. Which is why the jungle looked similar to the Amazon, then other parts looked like a Forest.
In both Predator decapitation scenes, the heads are lopped off in one clean stroke that severs the entire neck. In both cases, though, none of the aliens' tentacle "hair" is cut, even though it would be in the path of the blades.