Bobby finishes extracting two of his wisdom teeth with 14 minutes remaining. When he's in the next room he only has 4 minutes left.
When Bobby is trying to save Suzanne, he receives three sets of punctures in his sides. Later when he is trying to save his wife by crawling up the chains, the puncture marks disappear and then reappear.
(at around 1h 22 mins) In the flashback that shows Dr. Gordon writing the "I know who you are" note to Hoffman, the handwriting is clearly different when Dr. Gordon is shown writing it and when Hoffman is shown reading it.
(at around 1h 4 mins) When Officer Matt Gibson is searching for Hoffman, Gibson and the SWAT Team have their guns drawn, but in the next scene Gibson cycles the slide to put a bullet in the chamber, no cop would unload their gun and then load it again while searching for a criminal.
(at around 42 mins) After Bobby failed to save Nina, his face and shirt are covered in blood. Moments later when he walks into the next hallway, almost all of the blood is gone.
(at around 1h 4 mins) Bobby extracts two teeth to get the combination to the next room. When he looks at the teeth, the numbers are on the tooth root. To do this would be impossible without removing the teeth first.
(at around 12 mins) Officer Matt Gibson agrees to give Jill Tuck immunity in exchange for her testimony against Hoffman. However the police department doesn't have the authority to grant immunity, immunity can only be granted by the district attorney's office. The police are not allowed to promise a suspect immunity unless they have first cleared it with the DA's office. They can tell the suspect that they will recommend that the DA grant them immunity if they haven't yet spoken to them but they have to make it clear that it is not ultimately up to them.
(at around 2 mins) Dr. Gordon is shown using a steam pipe to cauterize his amputation. Proper cauterization typically requires temperatures above 900°C, whereas a steam pipe in a building is typically between 100-200°C. The temperature of the pipe would have been far too low to have any appreciable cauterization.
Hoffman's stitches disappear as the film progresses. This is due to the fact that the events of "Saw 3D" take place two months after the end of Saw VI (2009), and flashes back a couple of times at the beginning of the film to establish continuity.
(at around 21 mins) In the "Horsepower Trap", we can clearly see that the arms that are about to be ripped out from Dan, are in fact already "ripped out" and just hang there, waiting to be dragged by the car.
(at around 1h 22 mins) During the ending montage, when the Saw III - L'enigma senza fine (2006) footage of Lynn Denlon's surgery on John Kramer appears, a very quick reveal of a pair of fingers tossing fake blood onto her face appears from the left side of the frame. However, this mistake was not present during the original sequence in "Saw III".
(at around 21 mins) In the garage scene with Evan in the Car, it can clearly be seen that the arms that are about to be ripped out from the chained guy, are in fact already "ripped out" and just hang there waiting to be dragged by the car.
(at around 1h 2 mins) When the IA tech is trying to track down Hoffman's location by hopping through all proxies until it can find the real IP address, the ipconfig output of the tech's computer is seen in the background. When displaying the name of the IA network in the ipconfig output, that configuration property label is misspelled as "Desciption" instead of "Description".
(at around 1h 20 mins) When Hoffman is burning the Jigsaw evidence, you hear the click of the lighter as he opens it, he then drops the lighter into the gasoline on the ground, however you also hear the lighter closing again, though the lighter clearly never got into Hoffman's hands again.
Nina's trap could have been more easily solved if Bobby kept his hand over her mouth while pulling the string between his fingers.
It's never specified who found Eric Matthews, fit his broken foot into a brace, and feed him after he crawled out of the bathroom. (It was possibly Dr. Gordon, but this is left unsaid)