Plot hole: The entire purpose of the clone teams on earth was to service drones. When Jack enters the Tesseract, there are thousands of them lined up in niches in the bulkheads. Further, one would think the alien craft would have the ability to constantly replenish them by the thousands. So there is zero actual need for the clone teams at all. And for that matter, given the drone power cores are powerful explosives, they could just be used to explode on disablement or proximity to kill the humans nearby.
Plot hole: According to the flight recording, Odyssey was on an uncontrolled pull towards the Tet as Jack says, "We're not getting away from this thing." So even if Jack jettisoned the sleep module where Julia was in, the module should not be able to get away as the whole ship is being pulled towards the Tet.
Continuity mistake: When Jack sets up the motorbike, he pivots the two bars forward and locks them to form the handlebars. A few shots later as Jack looks down at the sensor, you can see one solid handlebar, all the way across. (00:13:45 - 00:14:25)
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. (00:18:40)
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. (00:22:35)
Plot hole: During the movie, bubble ships and drones are tracked by the Tet using a transponder or similar, and Tech 49 is tracked by drones via DNA tracing. At the climax of the movie, Tech 49 approaches the Tet in Tech 52's bubble ship along with a cargo that only Tech 49 would be carrying. Whether by DNA analysis, or simple logic, the Tet would have known it was actually Tech 49 in Ship 52, and it seems highly unlikely that this combination would have been allowed access to the Tet.
Factual error: When Jack retreats to the cabin for the first time in the film, he puts a Led Zeppelin record - Led Zeppelin II - and plays the first song on that side of the record, which turns out to be 'Ramble On'. Any Zeppelin fan would know that 'Ramble On' is song number 7 on side B, therefore the needle should have been placed somewhere in the middle of the disc. The first song on that side of the album would be Heartbreaker. (00:33:55)
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). (00:39:40 - 01:49:05)
Other mistake: When the alien drone is deciding whether to shoot or not, the screen showed that the operation system was in English. It should be in an alien language or have no language.
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. (00:19:10)
Audio problem: The scene after Victoria drops the plant from Tech 49 and lets it fall onto the Earth, shows the two of them having supper. The first line said in this scene is Victoria saying "Every day you have to go down there... And see what was lost." Victoria's lips don't move an inch when she says "and see what was lost." (00:24:10)
Revealing mistake: When Jack says "Screw you" to Sergeant Sykes, Sykes pulls his pistol and shoots Jack. You see the gun flash, and you see an impact on Jack. But if you watch closely, they do not line up. The special effects charge goes off indicating the hit on Jack's right breast. But when the gun goes off, while still moving, at that moment it was pointing at Jack's lower left abdominal region. (00:58:50)
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. (01:09:55)