(at around 1 min) During the beginning autopsy scene, the person performing the autopsy puts his mask on upside down (the eye splash guard is at his neck). As soon as the camera jumps, the face guard is positioned correctly.
(at around 46 mins) During the flashback in which Jill is attacked by Cecil Adams, as she is leaving the clinic, she has to unlock the door at knife-point even though she never re-locks it when retrieving the jacket. The door's lock is a deadbolt type and no knob is present, so it wouldn't lock itself automatically.
(at around 34 mins) When Officer Daniel Rigg enters the hotel room with the box on the bed, there is a photo of his wife on top of it. On the back of the photo, the words "she needed you" are clearly displayed in red ink. However, as he opens the box, you can see the that the back of the photo now reads "she needs you" instead from the letters "eds" at the edge of his hand.
When the scene with Agent Lindsey Perez on her way to the hospital ends, it shows Art Blank sitting at the desk with the timer on 19:47. Later in that scene he walks back over to the desk and the timer is on 19:39 when about a minute of the scene had passed.
When Rigg finds Jigsaw's last note for him in the desk drawer of the "FEEL WHAT I FEEL" room, it is first seen to have only one sentence: "Become the teacher and save a life." In a subsequent close-up, a second sentence appears: "Go back to where it all began."
At the end of the camera pan from the hospital room into the interrogation room, Jill's shirt is not fully buttoned as the character had to run from the hospital set into the interrogation set while changing costumes. It is corrected in the next shot.
When Agent Peter Strahm has his outrage, after he has called Agent Lindsey Perez's mother, the first time he knocks down the papers the computer screen shows "normal use". When they show the knocking over again zoomed in the computer screen shows the Windows welcome screen, then back to "normal use".
When the crime scene photographer gets accidentally shot by the crossbow in the classroom, the bolt hits the wall next to a red and purple flower. In the next shot, the bolt is at a different angle than before, and is stuck into the wall next to a different, gold and purple flower.
(at around 3 mins) During the autopsy, when the brain is taken out of the skull, it is not attached to the brain stem and spinal cord; it is loose in the skull. in reality, lots of dissections are needed for it to be done.
(at around 15 mins) When Officer Daniel Rigg is watching the interrogation video of Jigsaw's ex-wife he is looking at several books and magazines about Jigsaw. The book he picks up is titled "Jigsaw: Is He The Murderer The Police Say He HIS?"
(at around 1h 8 mins) In a flashback, John Kramer is shown abducting Cecil Adams at a Chinese street festival celebrating the Year of the Pig. The last two years of the Pig were in 1995-1996 and 2007-2008. This does not match Jill's statement that these events took place shortly after John's diagnosis with cancer in 2003.
Officer Daniel Riggs tries to free Brenda by shooting the motor. Yet it never occurs to him that with her hair wound tightly into a ponytail all he had to do in order to free her was put the muzzle of his pistol right onto the ponytail and pull the trigger, the bullet would rip through her hair and she would be free.
The goof items below may give away important plot points.
Incorrectly regarded as goofs
At the end of Saw III, when John died, he has no facial growth, and during his autopsy, stubble is clearly visible. Despite it being commonly believed that a person's hair can grow after death, it cannot. However a corpse's skin can recede allowing hair under the skin which grew during life to become visible.
(at around 1h 18 mins) Art Blank's second trap was the Spine Pincer, which was intended to slice through the back of his neck if he failed his test, but when he takes off his jacket (revealing the device) he bends his head and clearly shows that he can get his spine out of reach of the blades. The pincers have no extension, so Art really has no obligation and no reason to subject Eric Matthews and Mark Hoffman to their torture.