Continuity mistake: When William walks into the steam room, we see the tape player from William's point of view. The camera then looks at William and the tape player has rotated 180 degrees instantly. (00:50:25)
Continuity mistake: In the opening game, Simone's arm alternates from wet to dry depending on the shot. (00:03:30)
Continuity mistake: At the very start, the position of the meat cleaver on Simone's table changes between shots. (00:03:40)
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).