At 1 hour 28 minutes and 40 seconds, Paul is seen standing next to Chani his eyes are blue, in the next scene Paul's eyes are normal. At this point In the movie Paul has only been on the planet Dune for a few days, it takes years of extended exposure to the spice for ones eyes to become blue, like the Fremen. Which happens to Paul later in the movie.
When Jessica and the Reverend Mother Mohiam enter Paul's room before he is to be tested, their height differences change with each subsequent shot. Jessica is much taller than Mohiam in the first shot, much shorter in the next, back to being taller in the next, then the same height or shorter for the remainder of the scene.
When Paul is in the desert trying to ride the worm, the red coloring on the shoulders of the Feydakin are visible, but Stilgar did not mark the Fedaykin until before the Fremen started attacking the Spice harvesters, which happened after Paul had ridden the worm.
After Baron Harkonnen kills a young man in Giedi Prime, there is a head-shot showing Baron's face covered in black oil. Camera focuses briefly Feid Rautha (Sting) and then backs to the Baron, but his face is cleaner than before, and there is blood in the left side of his forehead.
Both, Duke Leto Atreides and his son Paul wear changing rank insignia on their dress uniforms. On planet Caladan, Paul wears an eagle, a star and a bar, as does his father and his friend Duncan Idaho, which makes no sense at all. During their space travel to Arrakis, Paul's epaulet sports an eagle and two stars, Leto's an eagle and three stars. This is logical, because the duke is one military rank above his heir. On Arrakis, the epaulets of their desert camouflage uniforms are the same as at the start of the movie.
During the first battle of the film Rabban is seen throwing Atreides' conscripts off of a bridge. When Rabban throws a man off the bridge you can clearly see the ground shake a few feet around the man as if he lands on some type of padding rather than solid ground.
(Extended version only) The shots of the Reverend Mother Mohiam traveling to Caladan to test Paul are reused shots of Jessica and Paul being taken into the desert by their captors after the Harkonnen attack on the palace. At one point you can see them both lying on the ground behind the pilots.
In the morgue scene in Arrakeen, the establishing shot shows two Harkonnen corpses, one in the foreground and one in the background. The body in the background adjusts his head to find a more comfortable position.
During shield practice, when Gurney slides across the floor, the face of Patrick Stewart's stunt double can be very clearly seen. Kyle MacLachlan's stunt double can also be seen when Paul slowly pushes his knife through his shield.
When Paul prepares to ride the worm he is surrounded by Stilgar and other warriors in the desert, some of them having red paint on their shoulders identifying them as the "Fedaykin".
AFTER the worm riding scene however, Stilgar is seen putting red paint on those same warriors and pronouncing them Fedaykin in a ceremony. This indicates those two scenes were filmed in reverse chronological order but edited together incorrectly.
The goof items below may give away important plot points.
When Paul tells Alia to go for the kill against the Baron at the end, she takes a swipe at his face with the needle weapon. As the Baron shrieks and reacts to the cut there is no hint of harm to his face, yet in the next shot of him floating backwards, he has a big bloody gash across his face from the cut.
As Paul walks into the room of prisoners after the final battle, Thufir Hawat is seen in the crowd behind the emperor. In the next shot, he's no longer there. He is suddenly seen again a few shots later watching the knife fight.
After the baron is struck with the Gom Jabbar and is flying through the air, a sandworm turns, opens its mouth and takes the floating baron. As the sandworm is turning and comes to a stop, the made-of-rubber creature wobbles like jello and looks, unfortunately, exactly like what it is: a miniature molded latex creation that is stopped too abruptly and jiggles like a slinky.