Having your back to the door (Motif)
At the beginning of Dune, Thufir Hawat berates Paul for having his back to the door, allowing people to sneak up on him. This is a motif throughout the novel, as characters are often described as being in a specific position in relation a door. Dr. Yueh has his back to the door, foreshadowing his betrayal by the Baron, and Paul has his back to the door when the Sardaukar attack him, Jessica, and Kynes. The Baron Harkonnen has his back to the door after narrowly escaping Duke Leto's poisoned tooth.
When he sees Hawat for the last time, Paul says, "As you can see, my back is toward no door." Hawat, however, responds with, "The universe is full of doors." He is communicating to Paul that one is never completely safe, and he's perhaps retracting his emphasis on that motif during training. Hawat's final message seems to be that no matter where you orient yourself in the universe, you're never fully prepared for the unknown.
Atreides portrait and bull's head (Symbol)
Duke Leto keeps a painted portrait of his father, the old Duke, and the head of the bull that killed him mounted in his dining room on Caladan; when they move to Arrakis, he has them hung in the dining room there. They bother Jessica to the point she won't eat in the dining room, but Duke Leto finds them a useful reminder of loyalty and bravery. The old Duke didn't have to fight bulls, but he chose to, and when the time came, he allowed the bull to kill him, which contrasts with the Harkonnen slave-gladiator pits where the fights are always rigged.
The presence of the painting and the head continues through the novel, but their meaning changes depending on who's narrating. For example, Thufir Hawat looks at them and thinks of himself as the bull, Jessica as the matador. The Baron Harkonnen, after killing Duke Leto, steals these objects and hangs them in the Harkonnen hall, where they give him a deep sense of foreboding. They inspire the Baron to wonder what Duke Leto thought when he looked at them, which is perhaps the only moment of genuine, non-manipulative empathy from the Baron.
Date palms (Symbol)
The 20 date palms outside the governor's mansion in Arrakeen are symbols that immediately communicate the scarcity of water, and how easily that water is wasted by non-Fremen on Arrakis. Every day, those 20 trees require an amount of water that could sustain 100 men. The water wealth displayed by caring for 20 date palms is enormous, ostentatious, and shows a lack of understanding of the planet.
When they arrive in Arrakeen, Dr. Yueh explains this to Lady Jessica, and she says they're looking at this place too critically. During the Harkonnen attack, the date palms are set ablaze to illuminate the mansion at night—all of that water not only wasted but burned thoughtlessly to the ground.
The Governor's Mansion on Arrakeen (symbol)
When he returns to the governor's mansion in Arrakeen after defeating Harkonnen and Sardaukar forces, Paul observes plainly to Stilgar and Gurney, "This place is a symbol." The mansion symbolizes to all people of Arrakis (and, now, all people of the known universe) who is in charge; it also symbolizes to them that Paul has won a complete victory, visibly claiming his status as Duke Atreides.
To the reader, the governor's mansion has that symbolism as well, but it also provides a symbolic bookend: Paul entered the governor's mansion at the beginning of the novel, young and gifted but unsure, and now he returns as a Fremen messiah, completing his "hero's journey" by returning to a point of "home." (If the story ended with Paul in this mansion, assuming his father's ducal seat, Dune might be a more traditional hero's journey, rather than a variation on one.)
Desert mice (Symbol)
There is a lot of animal symbolism in Dune, but arguably the most important is the desert mouse, the muad'dib after which Paul names himself. Muad'dib are exceptional survivalists, creating their own water and propagating widely in all parts of the desert. The Fremen call them instructor-of-boys and take great meaning from Paul choosing to name himself after a mouse.
In Book 2, Chapter 7, Jessica and Paul are alone in the desert at night, before encountering Stilgar and the other Fremen. Paul notices an "up-hop, jump, pop-hop of tiny motion" and deduces that they're watching mice in the dark. As soon as he makes this observation, a "ghostly gray bird" falls soundlessly on the mice and takes away "a small, dark shadow in its talons." Though desert mice are great at surviving, by behaving a certain way (jumping), they can be spotted and killed by predators, reduced from mice to small shadows. Jessica thinks: "We needed that reminder." The symbolism of the muad'dib and their interactions with the desert is apparent to readers, but it's also legible to Jessica and even Paul, who decides to become Muad'Dib but jump only when the time is right.
