(at around 2 mins) When Matthews' friend, Michael, is watching the puppet explain his situation on TV at the beginning of the movie, the channel indicator on the television keeps changing from displaying channel 3 in one shot to being covered up with duct tape in the next.
When the SWAT team arrives at Jigsaw's lair, the clock on the wall says 7:30. After the timer in the monitor room has gone down by 90 minutes, a shot of the wall clock shows the time as 8:00 - only half an hour later.
(at around 50 mins) When Xavier opens the door to the Syringe Pit, it shows a very short clip showing the timer on the door for the antidote. If you slow the clip down, you will see that the timer shows '4:00', in the next scene it shows '2:58'.
(at around 14 mins) When the SWAT team have their guns aimed at Jigsaw's heart (just after Matthews says "Hey - is this close enough?", we can see three laser guides on his chest. Then one of the SWAT team members points his gun down, but there are still three laser guides on Jigsaw's heart. Seconds later there are two lasers, then three again.
(at around 16 mins) When Detective Eric Mathews meets John his badge is normal. A few moments into the scene it becomes twisted and when it cuts to John then back to Eric after a second the badge is normal.
In the opening scene, Michael drops to his knees and screams "NO...NO...NO...NO...!" right before the death mask closes on his head. In Jigsaw's video, he never told Michael how much time he had, and the timer was on the side of the device where Michael couldn't see it, yet he somehow knew exactly when his time was up.
To fire a revolver the hammer must fall forward to drive the firing pin into the cartridge's primer. When the key is turned in the door we see the booby trap mechanism begin to cock the hammer of the revolver. But just as the hammer reaches its full rearward position, and before it falls forward, the revolver fires. Then the hammer falls forward.
(at around 1h 9 mins) In the hand razor trap scene, when Addison puts her hands in and Xavier has entered the room, blood is suddenly all over her hands, while when she put them in they were practically clean from blood. There is no way blood can cover her hands like that just by getting stuck like that.
The goof item below may give away important plot points.
When Gus is shot through the eye, the bullet goes through his left eye and has a pattern of blood running down his face, yet later on throughout the movie, when Xavier sees the number on the back of Gus's neck, we see Gus's eye is perfectly normal with no blood marks, or bullet wounds.