Other mistake: After Jeff gets the key from the Rack trap room, the shotgun fires and hits the judge. He is standing with the shotgun to his right, yet he is hit on the left side of his face. There is also an inconsistency with the timing. The gun fires, then the actor turns to reveal the wound on the left side of his face. It's easier (but in no way required) to see the glaring mistake with slow motion.
Other mistake: Near the end of the film when Jigsaw has the tape player, the 'play' button is near the left side. But Jigsaw's finger is on the right side, not even close to the play button. Jigsaw presses on the right side where there isn't even a button, but the tape begins to play anyway although nobody pressed the actual play button.
Answer: Adam didn't just lose because he let the key get drowned. He had the two hacksaws and he broke his own in a hurry. And there was also the toilet lid that he could have used to smash his foot like Eric did in Saw III. Jigsaw never said that improvising or thinking outside the box was against the rules. So even if you wipe the key out of the equation, Adam still has at least two other ways to release himself from the chains.
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