Other mistake: When Leo is laying his dead kids on the grass, the little girl keeps moving her eyes and breathing.
Continuity mistake: The morning after Teddy's light-flash migraines, he and Chuck walk out into the center courtyard and look upon the havoc wreaked by the thunderstorm. Teddy glances up at the electric wires around the gated perimeter and sees a branch that had fallen and bent the line. In the first shot, the log is leaning into the courtyard. The shot then cuts closer and the log is leaning outside of the courtyard. When the shot cuts back to Teddy, the log is once again mostly inside the courtyard.
Factual error: In the flashback, when Teddy was among the soldiers liberating Dachau, there is a semi-circular sign above the gate that says "Arbeit Macht Frei". Dachau had a sign with those words on it, but its sign was oblong. The sign at Auschwitz was that shape.
Continuity mistake: During the interrogation scene, a patient asks for a glass of water. When she receives a the glass of water, she lifts her hand to her mouth and makes a drinking motion, but is not holding a glass. A moment later she sets down an empty glass that previously she was not holding. When the camera angle changes, the glass has become half full. She also is "drinking" with her right hand and sets the glass down with her left hand.
Continuity mistake: In the scene where Teddy is about to blow up the car, at first you see him stuffing the necktie into the gas tank. As he talks to his wife, he remarks to her that he never liked the tie, and he holds the entire tie up to her. In the next shot the tie is once again fully stuffed into the tank.
Other mistake: During the flashback of the soldiers executing the Dachau guards, the soldiers are in a line opposite the guards who are in a line against a fence. The soldiers all start shooting at the same time, but we are shown the guards being mown down by gunfire in succession, like dominoes, rather than simultaneously.
Revealing mistake: In the very first scene, when Teddy and Chuck meet, they are standing on the bow of a ship traveling at full speed (as the Captain wants to return to the mainland before the storm hits), yet their lapels don't so much as flutter. Even at a slower speed, there would be some movement from the air as they passed across the water.