Continuity mistake: At Hoover Dam, when the soldiers salute Keller the clock reads 10:00, then as Keller, the soldiers, Maggie and Glen walk away in the background, when Simmons tells Sam that they got off to a bad start the clock reads 11:35, and next shot when Banacheck interrupts it reads 11:43. Also when Simmons talks to Mikaela and Sam the word "Nevada" is gone and it only reads "Time" under the clock. Then when Banacheck says, "Come with me, we'll talk about your car," the word "Nevada" is back under the clock.
Continuity mistake: After Gerry gets smacked in the face by the 'broken' suspender clasp, we see the silver clasp land under the dresser. Yet, when he's moaning and lifting his leg to get onto the bed, we can actually see the clasp still intact on the front suspender that came loose, which is dangling right behind him (just look between his legs). Of course, in the next shot, that clasp is gone. Since the silver clasp is one of the plot points, this is bizarre to say the least.
Continuity mistake: When John and Catherine are in the hangar at the runway, the Cessna's tail number is N3035C. When the plane is shown in the air, the number is N3973F. When they land, the tail number has changed back to N3035C.
Continuity mistake: In the bedroom scene the girl is holding a clear cup full of beer. The camera goes off her and when it comes back she is holding a blue cup. The camera goes back off her then on her and the cup is clear again.
Continuity mistake: When Sam is in his bedroom, after he finds the Cube sliver it falls and dramatically burns a hole through the floor into the kitchen. But Sam's bedroom is over the living room (there is nothing on the ground floor below Sam's elevated bathroom, and in the first movie Jazz hides in this open space), and the kitchen is actually located between the den and dining room, at the other end of the house. If they were to follow the actual floor plan of the house, the Cube sliver would have landed in the area of the piano in the living room, but where would the fun have been in that?
Plot hole: Joy and Sadness are stuck outside of the control center. They are trying to figure out how to get back, and encounter maintenance workers who are discarding old memories. The maintenance workers show that they have the power to send memories back up to the control center to be played. Why couldn't they send the core memories that Joy had back up the same way? Better yet, why not use that method to send Joy and Sadness back up to the control center? The director of the film is even aware of the plot hole, and said "Yeah, well then we wouldn't have a third act," before explaining how the idea of recalling memories was added in later, "box[ing] [the screenwriters] in a corner a little bit."
Continuity mistake: Charlie Brown is using a pen to write a book report. The black ink leaks and gets all over his hands. When he walks to his dresser to get a pencil, all the ink stains are gone.