Revealing mistake: Right before the Smokers show up, you can see land on the left hand side of the screen.
Factual error: The Mariner's gills that allow him to apparently breathe ocean water, are extremely unlikely. Even mammals that live underwater, like whales and dolphins, did not evolve gills. It is not possible for a warm-blooded creature to supply itself with enough oxygen using only small gills.
Factual error: Regardless of the type of event that caused the ice caps to melt, Waterworld, as shown, is impossible because: A. Scientists have measured that if all landlocked ice (Antarctica, Greenland, and the like) melted, the worldwide water level would not rise by anywhere near enough to cover the whole world in water. B. The melting of the North Pole ice cap would have no effect at all on the worldwide water level because that ice cap is already floating in the water (try putting an ice cube in a glass of water and letting it melt. The water level won't change). C. Unless the event that caused the ice to melt also altered the earth's tilt, the poles would still be cold and would refreeze, lowering the water level.
Continuity mistake: In the beginning when Mariner goes diving off his boat for sunken treasure, he fills a timer with a handful of small stones which steadily drop to bring up the diving equipment when exhausted. After the camera shows some scenes to imply time going by, you can clearly see the amount of stones fallen is equal to about ten handfuls of stones.
Factual error: When Costner spots the Smokers on their jet skis, his catamaran has no sails up and is dead in the water. He hastily puts up the sails and speeds away, outrunning the Smokers. This would be impossible in real life, from a standing start and light wind.
Continuity mistake: After the mariner escapes the atoll and begins turning the gunboat towards the deacon, we see the firing path pass the end of the atoll wall. A couple shots later, it shows four smokers on jet skis getting shot as they exit the main gate, which is in the center of the wall facing the attack and had already been passed by the firing path. (00:38:00)
Factual error: The Mariner takes Helen down to the sea bed in a makeshift 'diving bell'. He tells Helen there is only enough air for one person. The depth they dive to is shown as quite comfortably exceeding 200m. (To save this turning into a science essay I'll include this link: http://en.wikipedia.org/wiki/Boyle's_law). Regardless of suspension of disbelief, there is no way that a bell of that size would carry enough air for even one person at that depth for that long.
Factual error: The Mariner's tiny gill-slits behind each ear could barely oxygenate a one-foot-long fish, never mind a full-grown human being. To accommodate his 6-foot body, the Mariner would need multiple 8-inch gills stacked on either side of his neck, at least. Compounding this error, the Mariner then draws Helen to safety underwater, telling her, "I'll breathe for both of us!" So, now his grossly undersized gills are oxygenating two full-grown human beings.
Factual error: The Smokers' plane is shown with every surface completely rusted reddish-brown. But planes are made from light alloys, not steel. They can eventually corrode - very slowly - but the film of corrosion is white, not red like iron rust.
Continuity mistake: When Mariner is knocked into the mud pit while in the cage we see that it does indeed sink. However as the woman and the girl are crossing the bridge to get to the windmill, the camera cuts to Mariner in the cage. The cage has sunk so that he only has room for his head and shoulders. Then as the woman and girl run past him there is another shot in which the cage is now further out of the mud and Mariner has room for the majority of his upper body.
Revealing mistake: The Mariner had just been ignominiously catapulted off the mast of his boat as a result of the tethering rope breaking loose from the circling airplane. In the scene showing him climbing back onto his boat land can plainly be seen on the right side of the frame. This occurs just prior to Helen saying: "Oh, I'm really sorry". (00:57:25)
Continuity mistake: After the Mariner rescued Enola, the Deacon and his goons collide. As the fireball of their collision comes up, their wakes are still visible. A second later, the fireball is still growing but the wakes have totally subsided. Not possible given the explosion is only several seconds old.