Riddick "forgets" the exact number of stars which surrounded M-344/G, the planet on which he crashed with John's during the initial film in the trilogy, Pitch Black. He tells Boss it two stars, when the film clearly showed that it had three,
When Riddick is trying to get past the creature to the other side of the planet, the water in front of the stairs is deep enough that two of the creatures (one very large) can be fully submerged in it. However, when he runs back with the dog, it is shallow enough that he can slide across it without trouble.
When Riddick is about to push over the obelisk, to create a hiding place so he can sleep, there are a few rocks in the hole he will hide in. In the next shot, as the obelisk is falling, the hole is empty. He wouldn't have had time to clear out the hole as the obelisk was falling.
A character claims to track Riddick using some device that has detected human pheromones. Since Riddick has been established to be Furian, he wouldn't have human pheromones. But humans don't release or even have pheromones, anyway. Humans respond to odors released by bacteria that live in sweat.
We're lead to believe the power nodes for the two ships are different, both by dialog and in physical appearance. When Riddick spies on Vargas using Dahl's mirror, the nodes in the rack indicates that Vargas is on the wrong ship.
When loading the tracking rounds, Dahl has to move the sights on the rifle each time to clear the chamber and load the next round. Later, using the same rifle and the tranquilizer rounds she is able to eject and reload without moving the sights.
When Vaako reveals that the world he'd visited as a young Necro was Furya, he does so by stating that the Furyan warrior had eyes just like Riddick's. However, all previous lore in this universe accepts that Riddick's eyes look the way they do because of a surgical procedure ("a surgical shine-job") - they are not a species/race trait.