Continuity mistake: The amount of Petrol that Hoffman chucks over the FBI lab, Perez, and his boss, is more than what could be in the single container we are shown. (01:09:00)
Continuity mistake: We are shown a clip at the end of someone putting the reverse bear trap on Amanda in Saw. However, the device is not the same one as seen in Saw. Note the mouth section. It is a lot thinner than in Saw. (01:17:50)
Continuity mistake: Jill opens the 6th envelope to show Hoffman. When she does, the envelope instantly vanishes from her hands. (01:18:25)
Chosen answer: The trap wouldn't have worked if William stood on the other side of the cage. When William walks towards the mother and son, you see a closeup of his feet stepping onto a pressure-pad that activates the trap. If William stood on the other side of the cage, the trap would never have turned on because the pressure-pad would not have been set off, and nobody would have died. Also, even though Jigsaw pre-plans his traps, there certainly are circumstances where the mother and son could have gotten hurt. One must remember, Jigsaw is insane, and it's shown repeatedly in the series that even though he intends to help people, he is not above sacrificing people or putting innocent people in harm's way to teach his subjects a lesson. (The most prominent examples being the mother and daughter from the original film and Joyce from "Saw 3D" who were innocent but placed in direct danger to be a motivation for the subjects).