Donnie Wahlberg (who plays a major role in this film, as he has in the past two films) was not secure until 2 days before shooting began. It was suggested that his character be replaced by another character just in case, but director Darren Lynn Bousman persisted, and eventually secured Wahlberg. See more...
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Continuity: Rigg pulls the red scarf off the blonde woman and we don't see where it goes. Then there are two closeups of the woman where the scarf is nowhere in sight, and she has nothing on her left shoulder. Then in the next shot, suddenly the scarf is covering her and the machine behind her, and part of it is draped over her left shoulder.
Continuity: When the guy with the mouth stitched shut has put his legs against the machine to avoid being pulled anymore, a few seconds later you see him with his mouth open, enough for him to easily say something. At the end of the scene you see him being able to open his mouth easily, something he could've then done much earlier. And even if say his tongue was cut out to explain him not being able to say anything with an open mouth, he wouldn't be able to scream at the end either.
Continuity: When Agent Strahm has finally realised where the final game is being played, he holds up the piece of paper of Jigsaw and Art outside the Gideon building. There is a hand at the top of the picture, which is a newspaper clipping, but he is holding a picture, not a newspaper. This is a reused shot of when he shows Agent Perez the picture earlier in the movie.
Other: In Saw II, Jigsaw shares a story with Detective Matthews about how he attempted suicide after his cancer diagnosis by driving his car off a cliff. We then see Jigsaw pulling a metal rod out of the left side of his stomach. However, no puncture wound/scarring is visible on Jigsaw's stomach when his autopsy is being performed.
Factual error: Several mistakes about the clock in Jigsaw's workshop: around 300 years ago the first pendulum clocks were built. They were completely different by size and design than this one, so the claim that it is so old is completely wrong. Real pendulum clocks like the one seen in the movie never have a second hand from center. You can also see by the movement of the second hand that it is a modern, battery operated quartz movement. This also means that the ticking you hear is not created by the clock itself but was added later.
Revealing: When Cecil's face is being cut by the Knife-chair, the first time he comes into the blades, it is painfully obvious that the blood is being pumped through the knives, and that his face is not being cut. You can even see his bloody, yet cut-free, face almost come through the knives for at least two full seconds, before there is a flash-frame jump-cut, and a number of deep cuts magically appear on his face.