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.
Suggested correction: It can be assumed that the jettisoned module has enough "jettison power" to force it away from the command pod. And in turn that force would move the pod further towards the Tet. It's reasonable to assume the Tet couldn't pull the module that was moving away, under dramatic force, and to which it didn't have line of sight (which was blocked by the pod).
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: 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.
Suggested correction: DNA analysis will not see a difference between Tech 49 and Tech 52 for they are clones, i.e. genetic identical.
Plot hole: Throughout the movie we see Vika monitoring Jack through the cameras and sensors on his aircraft, however, during his entire fight with 52 she just happens to be AFK and doesn't notice that what is effectively a doppelgänger has taken out her partner and commandeered his aircraft?
Suggested correction: At that point they are outside her sensor range.
There's no evidence to support the claim that they are outside her sensor range.