The film opens with a Sardaukar war chant. This chant is heard later in the film on the Sardaukar world of Salusa Secondus, used as a rite to prepare the warriors for battle. This chant is thus used to prepare the viewer for the film's experience.
The Sardaukar are hyped up as the Emperor's elite troops, and depicted as a warrior cult. When we see them on their homeworld of Salusa Secundus, the world is depicted as a stormy wet planet. This foreshadows how unprepared they prove to be for desert survival and combat with the Fremen, despite handily outmatching the Atreides household troops.
When Leto presses his signet in wax to accept the stewardship of Arrakis, you can see the Bene Gesserit scowling. He has literally sealed his fate.
The Atreides, who are supposed to be inspired by the Greeks, arrive and enter Arrakis with ceremonial bagpipes, an instrument-symbol associated with Scotland. Note, however, the Atreides' music have a mediterranean Toros y Flamenco flair to them, and bagpipes are popular in Galicia, northwest Spain (bagpipes are originally a Persian instrument, and only migrated to northern Europe later with the Romans, Scotland is actually one of the last places where Bagpipes were introduced). It also invokes European colonialism (Britain being the most important European colonial power), as it is an instrument that is alien and contrasting with the rest of Arrakis.
Also also, the Atreides' home planet is Caladan, suspiciously close to 'Caledonia' i.e. Scotland. What we see of Caladan in the film might very well be northwestern Scotland (it was actually shot in Norway, but the biome is very similar).
While mentats are not directly explained, they are still present. Because of this, Paul's status as a mentat is not mentioned in the film, but he does prove to be very Good with Numbers and have an excellent memory; during the harvester disaster, he quickly rattles off the weight of unnecessary equipment they can jettison to rescue the men.
Doctor Yueh demonstrates his skill as a physician - and knowledge of human anatomy and, furthermore, the limits of limb movement - by precisely hitting Leto's shield between his shoulder blades, where the shield-drilling projectile can work its way through the shield without Leto being able to swat it away, like Duncan demonstrates when the same kind of projectile hits him from the front.
After Duncan returns from his excursion among the Fremen, he's clean-shaven, whereas Duncan had a beard when he left Caladan (and actor Jason Momoa habitually sports one). With the mouth filter on a stillsuit, while experienced users like Stilgar can maintain a beard while wearing them, for a newbie to Fremen ways like Duncan, shaving the beard off would be easier.
The script actually has Duncan's beard be a significant detail in establishing the truth of Paul's visions: in it, the exchange where Paul talks to Duncan about his death, he notes that Duncan was clean-shaven, but Duncan takes this as evidence that the visions won't come true, as he likes keeping his beard. However, at a party to celebrate Duncan's departure that night, Leto asks that Duncan shave in order to look more presentable when representing the Atreides on Arrakis, with this being a moment where he and Paul realize (but are afraid to admit) that Paul's visions may be the truth.
When Paul trains with Gurney, he switches from the longer blades which the Atreides are shown to typically use, to a pair of shorter daggers, perhaps a means of visually foreshadowing that he will be skilled in using the smaller crysknifes when he arrives on Arrakis; in his vision of a future battle against the Sardaukar, Paul also sees himself wielding two knives at once.
We get a visual representation of how the cute Muad'Dib mouse gets its daily moisture: condensation off its huge ears! Real-life Earth beetles in the desert have been known to do this with their antennae.
Paul stepping up to be his mother's Champion when Jamis challenges may be him using his visions to attempt Defeat Equals Friendship. Unfortunately, he didn't know it was a Duel to the Death.
Baron Harkonnen retains his ability to float around like in the Lynch adaptation, but now wears a very long robe that trails to the ground even while he's up near the ceiling. While this could be as simple as him wearing a decadently luxurious outfit (in contrast to how Duke Leto dresses in practical military gear), it also makes him resemble the worm-human hybrid God Emperor Leto II from later in the book series. This makes for excellent foreshadowing, as Leto II is the Baron's great-grandson.
It might also be a means for the Baron to visually evoke a sandworm, highlighting his lust for control over Arrakis—he desires the planet's resources so much that, consciously or unconsciously, his clothes have begun to mirror one of the most distinctive creatures on that world.
In the book, the Sardaukar taking part in the assault on Arrakeen disguise themselves as Harkonnen or Atreides troops to sow confusion and hide the Emperor's role in the battle. In the movie, they go into battle as they are, making no attempt to disguise themselves. This jibes with the orders Liet-Kynes is given to "see nothing." The Emperor is so powerful he doesn't even need to disguise his troops, simply make everyone on the planet too afraid to speak up about what they saw, lest they get the knife next.
Paul tells Duncan that if he won't go with him to the initial negotiations, Duncan will die. Had they gone together, Paul would have been exposed to spice sooner, and had a few more weeks to familiarize himself with the awoken potential. The whole battle might have gone differently.
When you think of it, it makes perfect sense for Kynes to be the one character gender-swapped into a woman in the adaptation. Within the books, men hold every visible position of power, but the women (most of them Bene Gesserit) pull the strings behind the scenes and in many ways, are the real movers and players of the long game. Which is... kind of what Kynes does: he (or, in the movie, she) pretends to be just an official of some local importance and little standing, while running a secret long-term project behind the backs of nominal authorities.
Throughout the movie you would notice that Fremen are capable of taking on Sardaukar troops despite having a disadvantage of no personal shielding. You would then notice that their main advantage is stealth and effective use of the terrain. In an early discussion about shields, Harvesters do not have them because they attract Sandworms more than without them. In other words, their camouflage is their best form of protection while personal shielding would make them detectable, let alone easy worm food.
It could also reference a bit from the novel altered for the film. In the book, the Fremen think Paul is toying with Jamis in their duel because Paul's reflexes and training are attuned to shield fighting. Thus, his attacks are slow enough Jamis is easily able to parry or dodge, but Paul is so lightning-fast on defense it's obvious he has leagues of skill over Jamis. If the Sardaukar are similarly used to shield fighting, their attacks would be pitifully slow and weak to Fremen, used to fighting on Dune where shields are worse than useless.
Duncan's death scene can be interpreted as foreshadowing his fate in the novels, as he seemingly dies from a sword thrust, only to then stand back up and keep fighting before truly dying. In other words, even in his first proper death, he doesn't quite stay dead, paralleling how he's repeatedly resurrected in the sequels.
Jessica notes the Bene Gesserit have been to Arrakis and prepared its people to be receptive to members of their order. Later the Reverend Mother asks that the Baron allow Jessica and Paul the dignity of exile. He thinks he's being clever by sending them in the desert to die, but considering the Reverend mother knows about her order's preparation of Arrakis, and specifically asked for exile, he's basically doing what she expected.
Some Fridge Nightmare Retardant with the Baron’s hovering. It's rather unnerving... until you remember he has the hover tech because he’s too fat to move normally.
