Plot hole: Julia dies in the underwater escape trick tank because the axe couldn't get her out in time. However, if she was able to open the lid from inside the tank, get up, over, and down, then close the lid (all quickly, silently, and without assistance) when the trick goes properly, then there is no reason that the four men standing around could not have simply lifted the lid, either acting a key in the fake padlock to preserve the trick, or using a key if it's real. At this point she could have gotten her head above water and draped her hands over the side of the tank to stay up. That done, the crisis is over, and she must only wait to calm down enough to get herself down, or be assisted. Cutter built the tank, so he knew how strong the glass was. The only explanation for using the axe was to allow Julia's death, thus advancing the plot.

Continuity: Hugh Jackman puts a tan vest on twice in the scene when we first meet his wife.

Revealing: When one twin (presumably Alfred) is removing the other twin's fingers, "Alfred's" upper arm passes through his twin's head as "Alfred" reaches for the hammer.

Visible crew/equipment: When Angier goes to Tesla's laboratory and walks to the gate, on the far right side of the fence a figure can be seen, apparently holding something ahead.

Continuity: When the hotel clerk show Angier Tesla's machine in its box, he has his hands behind his back, and then moves them in front of his body. Yet when the camera cuts to behind the clerk, his hands are still held behind him.