Continuity mistake: When Cooper is driving to the coordinates the shot from inside the cab of his truck shows he using the interior light to follow his map, the next shot shows the truck driving away with the light off. (00:22:00 - 00:24:00)
Continuity mistake: Thomas takes the blade of Theresa at the top of the tower. When he does, his grip on the blade changes position and the hand changes too. (00:55:30)
Continuity mistake: Just after the captain's death, a close-up on Bill's watch shows its date as '11 07'. At all other times, it says '1 18'.
Continuity mistake: When Kat is asking the detective what he thinks happened to her mother, after Kat is in college and she visits home, the detective lights a cigarette. We see him move the cigarette out of view and when he brings it back there is barely 3 or 4 drags left. The camera cuts to Kat and back at the detective and there's over half of the cigarette left now.
Continuity mistake: When the plane is on the ground, it has two engines. When it takes off, it has four.
Continuity mistake: When Newgate is feeding the blind woman in the asylum, the position of her hands on him when he is pretending to be her son keep changing from the chest, to his neck, to his head.
Continuity mistake: Roy is on his back at one point, seemingly knocked out. A shot later he's suddenly on his stomach before regaining consciousness.
Continuity mistake: The amount of beer in Clinton's (and in Greta's) glass fluctuates. For example, Clinton's glass is almost full, but is even closer to the rim the second time it is shown. After the amount decreases (even though he isn't shown drinking any), the amount in his glass is fuller again. (00:45:20)
Continuity mistake: The car the hybrid man pushes is in OK shape at first, then he lifts and flips it through the copper fence, and now its whole front side is gone. They might used an already wrecked "car double" for the scene when it crashes and explodes. (01:40:50)