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.
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.
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: 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: 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.
Answer: Sealed stuff floats. They gather stuff just like the mariner.