(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.
When 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.
Hoffman's stitches disappear as the movie goes on. This is due to the fact that the events of Saw 3D take place 2 months after the end of Saw VI, and flashes back a couple of times at the beginning of the film to establish continuity.
(at around 1h 4 mins) After Bobby has extracted his teeth to obtain the code for the door, the numbers are seen etched on the roots of the teeth. It would be impossible to do so without first cutting open the gums.
(at around 21 mins) In the garage scene with Evan in the Car, we can clearly see 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 the end of the film Dr Gordon traps Hoffman in the bathroom from the first film as the room has never been discovered during the police investigations. However, this would mean that the police force did a terrible job investigating the house from Saw II with the trap door in the safe room which leads to the bathroom from Saw.
When Hoffman inserts the metal rod in Jill's mouth through the front of the reverse bear trap he then tightens three bolts with a spanner. However it is clear that only one rod is in place. When the device then snaps open we see a total of 9 rods on Jill's upper and lower jaws.