Continuity mistake: When Jack pulls out his motorbike, his Tech 49 suit is completely clean. When he stops the bike around a minute later, his suit is completely dirty despite just riding. (00:13:55 - 00:14:45)
Continuity mistake: When Jack brings Julia to Tower 49, she is in Sleep Pod 06. When the Odyssey playback is shown, she is in Sleep Pod 8. (00:40:41 - 01:45:49)
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.
Continuity mistake: During the chase with Jack and Julia, the glass door on Julia's side gets cracked by one of the drones. At the end when Jack shoots the drone, just before they eject you get a good look at the glass door next to Julia and it is undamaged in anyway.
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. (00:14:20)