Continuity mistake: In the latter half of the movie, Picard looks at a picture of himself from his days as a Starfleet Academy cadet while Beverly looks on too. This picture is actually the actor Tom Hardy (Shinzon, Picard's clone) and he appears with a completely bald/shaved head. Showing Picard bald as a cadet completely contradicts the TNG series. In the TNG episode 'Tapestry', a flashback set in 2327 (the year Picard graduated from the Academy), Picard is shown with a full head of hair. Also, in the TNG episode 'Violations', a flashback set in 2354 shows Picard with a partial head of hair when he takes Beverly to see her dead husband Jack's body. Or... Picard simply shaved his head at one time when he was a cadet and it grew back.
Visible crew/equipment: When Picard, Data and Worf are on the planet, just a few shots after they leave the shuttle, Picard drives a sharp left curve. If you look at him in this shot, it is not Patrick Stewart sitting on the driver's seat, but his stuntman, who is not even wearing goggles.
Continuity mistake: In the scene where Picard and Data are about to board the Scorpion attack flyer, Picard throws his disruptor rifle to the ground. Yet just seconds later when the Scorpion is about to escape by blasting the entrance to the hangar bay open, no disruptor rifle is seen on the ground.
Revealing mistake: Near the end of the film, when Picard bends the pole down to stab Shinzon, the pole supposedly goes through him and out the other side, but the prop travels several inches down his waist. A shot later, you can see the prop pushing against Shinzon's clothing, obviously not piercing anything.
Continuity mistake: Shinzon's outfit changes between shots near the end of the movie. When he is projected via hologram into Picard's ready room, and during the first half of the battle with the Romulan warbirds, Shinzon's shoulder pads are pointed. Halfway through the battle, the shoulder pads change to smaller, flat ones.
Revealing mistake: In the scene just after Picard, Worf and Data arrive back on the ship with the android parts, while examining B4 Geordi is using a static prop tricorder (The tricorder is soundless and lightless) and when he closes it you hear the plastic prop closing, not the typical clicking tricorder sound.