Revealing mistakes: When Piter stabs Dr. Yueh in the back, the knife is quite obviously tucked under Yueh's left arm.
Continuity: 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.
Continuity: Jessica's pregnancy seems to progress and recede without any regard to chronological order.
Revealing mistakes: The computer generated "'thopters" have fans on the back wings to make them fly. The actual close-up models are missing these fans.
Revealing mistakes: 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.
Revealing mistakes: 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.
Continuity: When Paul and his mother are stranded in the desert, Paul has several days' growth of beard. When he is rescued on board the 'thopter and is strapping in, he is clean-shaven. When he arrives at the caves, the beard is back, and when he leaves and is aboard the 'thopter, he is clean-shaven again.