Continuity mistake: The blood stain on Riggs' white shirt around the neck has blood under the collar, then at the end it is over the collar and has increased in amount.
Other mistake: 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.
Visible crew/equipment: As Jill is being interrogated, when it cuts to a shot where the two cops are looking at her through two way glass, a camera man is visible between them and the boom mic is seen at the top left hand corner, very faintly.
Plot hole: When Rigg is listening to the tape in the first hotel room, the tape instructs him to wear the pig mask in order to conceal his identity from the hotel cameras. Rigg wasn't wearing the mask when he entered the hotel, so putting the mask on after the cameras have already seen his face would do absolutely nothing to conceal his identity.
Revealing mistake: When Rigg shoots Art, just before that you can see Art shouting. Look at his chest. The bullet wound is already there (no slow-mo needed).
Revealing mistake: 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.
Revealing mistake: When Art is hitting the Trevor (the blinded man) character with the hammer/hatchet in the beginning, if you look closely, you can see blood coming from Trevor's head, yet there is no wound or cut. The blood is actually coming from the prop that is hitting him in the head.
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.
Continuity mistake: When Rig opens the door the clock says 00:00 time left, but when he is talking to Art on the floor the clock says 00:01.