Continuity mistake: After he discovers the beacon for Drone 172 was a trap, Jack takes off and leaps back over the gap he came from moments before. The camera angle behind him as he is about to hit the other side shows his arms down as he is bracing for the impact. But it cuts to in front of him and instantly Jack's arms are up in the air. He is not moving them up as the shot cuts.
Continuity mistake: The first time we see Julia's stasis pod number is through the gun scope and back at the tower shortly afterwards, and it is numbered 06. But in the flashback late in the movie after he says "dream of us" to her before launching that module, the pull back shows him leaving pod 04 (we can't really see the number, but the other pod numbers from left to right are 05 and 06 as he leaves that module, so 06 definitely isn't launched).
Continuity mistake: As Jack attempts to escape the abandoned library, he attaches himself to the cable which sends him shooting up. The cable snaps off and Jack falls back into the library. As this happens, there is a rope attached to his gun. But the rope vanishes by the time it falls into the pit a few seconds later.
Continuity mistake: Just after Drone 109 disconnects itself from the garage, the scene cuts back to Julia watching Jack and Victoria's argument. In the first shot, she is standing next to the ship with her shoulder partially behind the ship door and her head resting on the door frame. But in the next shot, we can see Julia to the left of screen with her shoulder now out of the ship's door and her head no longer resting on the door frame, standing a few inches further away from the door.
Continuity mistake: Just after Jack reads the quote from the Lays of Ancient Rome book, Victoria walks half way down the staircase and says "Jack." During this shot, Victoria is visible to the left of screen with her right hand placed on the banister and the rest of her arm bent downwards in a 6 o'clock direction. Yet in an instant close-up of Victoria, her right arm is now stretched in a 9 o'clock direction.
Continuity mistake: When Jack is riding his motorbike past the deserted ships, there is a huge trail made on the ground. This trail continues to be made as he rides. But as soon as he drives over a hill and stops his bike, there is no visible trail in the background, only the ships are visible.