Continuity mistake: After the scene with the pig gut pit, Jeff and the judge leave the room and the judge's clothes are suddenly not wet and almost clean. (01:17:15)
Continuity mistake: Right before Lynn says "I don't know what you know, but my marriage has survived more suffering that you could possibly imagine" her hair is all pulled back behind her ear. As she's saying that line you can now see that a noticeable amount is hanging on the side of her face and across her ear. (01:25:50)
Continuity mistake: When Jigsaw says "You're already dead on the inside", the oxygen mask is resting on his chest. In the next shot he is holding the mask. (00:25:00)
Continuity mistake: The key is bubbling when it first drops in the acid, and continues bubbling throughout most of the scene. As Jigsaw's message is winding down, the bubbling dies down and stops. But it's bubbling full force again when the detective goes to put her hand in the jar. (00:13:20)
Continuity mistake: The acid is completely red after the woman puts in her hand. The acid jar is then completely clear throughout the rest of the scene. (00:16:50)
Revealing mistake: When Lynn is inspecting the "reverse bear trap", the trap Amanda was placed in for the first movie, you can see a small orange light reflecting off a few surfaces, like Lynn's arm and the nearby table. This is the brightness level auto-adjustment light that is present on many handheld cameras, which the cameraman apparently forgot to cover or turn off. (00:47:20)
Continuity mistake: When Jigsaw is coughing up blood, the blood in the mask disappears between shots. (00:37:55)
Revealing mistake: It's obviously a fake head when the doctor is drilling the skull as indicated by the increased amount of hair as compared to facial shots of Jigsaw. (01:02:20)
Continuity mistake: There is a far-away shot when the first pig comes out. You can see Jeff standing on the platform holding his left hand to his face, there's an instant cut to a close-up of Jeff, but now his right hand is held up to his face. (00:58:45)
Continuity mistake: The blood streaks on the chained man's chest continually changes from almost covering his chest, to less noticeable. They probably tried to give the appearance of his continual bleeding, but the shots didn't make it into the movie in sequence. (00:06:25)
Continuity mistake: In the first shot of Kerry watching the Jigsaw tape you can see 2 folders to her left. She fast forwards the tape a bit, the shot cuts back to her, and one folder is inside of the other. Also, all the pictures spread out in front of her change positions and placement drastically. (00:12:00)
Continuity mistake: When Amanda takes some items out of her box, she lays a red cloth on the bed and then places some items on it. She places a razor blade down on the cloth and there is a large crease underneath the blade. Cut to another shot and the cloth is completely smooth; no crease. (01:07:50)
Continuity mistake: When Kerry reaches up the second time to try and get the key you can see the acid burns (a few, but not a whole lot of blood) on her hand. There is a quick cut where her hand is poised over the jar of acid and her hand has suddenly become almost entirely red and bloody. (00:06:10)
Visible crew/equipment: Just as Jeff and the judge walk out of the pig room, we see the judge walk through some plastic. When he walks through the camera is reflected on his back. (01:17:15)
Continuity mistake: When we first see Kerry in the Angel trap her arms are down by her side. The camera zooms out and now her arms are raised. (00:13:15)
Continuity mistake: When Kerry walks into the room at the start of the film, her ID is twisted. Camera switches to a long shot and it's not twisted. (00:05:45)
Answer: It was too late for Adam to solve the game the way he was intended to- the key went down the drain, which Jigsaw actually didn't intend to happen. Adam's key was meant to be tied around his neck in such a way that neither him nor Lawrence would be able to see, and Adam would be allowed to go free and escape if he were to locate the key- which would only be possible if he looked at himself. The whole idea behind his puzzle was "looking at himself instead of others, for a change." The reason it went down the drain instead, was because of Amanda, who continuously made traps unsolvable. Instead of tying it around him like Jigsaw asked, she just tossed it on his chest, which defeated the whole purpose. Also, he was given a saw just as Lawrence was, as a much more violent plan B, another way he could save his own life.
That doesn't make sense because Jigsaw told Adam that the key is in the bathtub at the end of the movie.