After the vehicles land at the harvester to pick up its crew, we see the crew run to the 'thopters. When Paul walks back in the 'thopter you see no prints going to the vehicle, only the prints from those who stood outside.
When Paul and his mother are standing on the top of a dune at the beginning of the film, there is a fold/crease in the backdrop behind them.
Just before meeting Dr. Yueh to comfort him, the concubine walks on what appears to be a marble floor, but her footsteps make loud sounds that show it is a lifted wooden floor.
The moons in the background never move (because they are on painted "translights"). The most noticeable example is out of the Arrakeen palace window. The moon never moves from its position through a gap in the shield wall for the entire duration of the banquet.
In the very beginning, when Paul dips his fingers in the bowl of water and flower petals, the water can be seen clearly moving in the bowl, even though it has not yet been touched.
When Dr. Kynes is talking to Paul in the observatory when his blue eyes are glowing, you can see the ultraviolet light used to make the glow reflect off his shoulder pad when he turns away and then the light blinks off. This also appears in the dinner scene when Kynes talks to the Guild Representative about carrion birds. The UV light reflects off his tunic and then turns off.
When Princess Irulan arrives at the Atreides party, she is introduced as "Her Royal Majesty". Majesty is a title reserved for the Sovereign, i.e. the Queen/King/Emperor. A Princess would be referred to as "Her Royal Highness", as Duke Leto does a moment later.