Continuity mistake: Lynn explains the procedure she's going to do to Jigsaw, then goes to fill the syringe. Look at the syringe when she sticks it in the bottle, the plunger part is pushed all the way to the bottom. The shot cuts to a different view and the plunger is a good inch or 2 pulled back already (she hadn't started to draw it out yet, you can see 1 or 2 inches of air). The shot cuts again, and now the plunger is at the top of the syringe again, then she starts drawing it out). (01:01:30)
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: When Lynn is operating on John's head, she the skin from the skull and then clips off some veins. Right when she asks Amanda to fill the syringe with alcohol to clean John's head, Lynn turns back to wipe up some of the blood, but there are no clips in place. A shot after that, we see her taking the syringe from Amanda's head and squirting the alcohol on John's head and the clips are there. (01:03:05)
Continuity mistake: When Lynn cuts open Jigsaws head, she clips off some veins with clamps and lets one fall in front of his face. A scene change to the front of his head shows no such clamp lying across his face. (01:03:05)
Continuity mistake: The blood splatters on Lynn's face change throughout the whole brain surgery scene. The splatters go from defined, to smeared, and then back to defined again a couple different times. (01:03:15)
Continuity mistake: The amount of blood on Jigsaw's skull changes drastically from thick dark red to thin almost translucent red. This is before Lyn clamps off the blood vessels and uses the alcohol to clear the area. (01:03:20)
Continuity mistake: When Jigsaw is in the process of passing out (after surgery) Lynn's hands move off the bed, back on, then off again, then back on (it wasn't just her moving them naturally, they were in the EXACT same positions each time they were back on the bed). (01:04:00)
Continuity mistake: The drill that Lynn uses on Jigsaw's skull has a white piece of tape on the end of the drill bit a short distance from the end, presumably to mark the thickness of his skull so she knows where to stop. In one shot (during the drilling scene) the piece of tape moves a good two inches farther up on the drill bit, but it's back down in the very next shot. (01:04:05)
Continuity mistake: In the close-up shot of Lynn removing the piece of Jigsaw's skull you can see that she's holding the instrument in her left hand (look at the position of her fingers), but in the farther away shots she has it in her right hand. (further evidenced by later in the scene where you see a close-up and she's still holding the instrument in the left hand and a knife is in her right). (01:04:30)
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: Amanda's sweat marks and eyeliner runs constantly change shape and size (bigger, smaller, and back to bigger) during the bathroom flashback. (01:10:30)
Continuity mistake: The red "blood" marks on Jigsaw's left hand change several times (smaller, larger, smaller, larger again) during the bathroom flashback. (01:11:10)
Continuity mistake: When Amanda goes to take off Adam's boots (in the flashback) his feet are spread a good 2, 2 and a half feet apart, yet when she goes for his right boot his feet are all of a sudden less than a foot apart. (01:11:30)
Continuity mistake: Amanda freaks out and pins Lynn to the wall after Lynn says "He doesn't even know you're there". Amanda's hand is around Lynn's neck, choking her. The screen cuts to Jigsaw very briefly (all he says is, "AMANDA!"), then back to Amanda, now Amanda's hand has moved up to being on Lynn's chin. Not only would moving her hand from Lynn's neck to her chin not serve any purpose, but the screen cuts happened too fast to allow for the hand movement. (01:14:25)
Continuity mistake: In the close-up when Amanda goes to suffocate Adam with the plastic, the plastic only goes up to his forehead, yet when the scene cuts back (instant cut) the plastic is completely surrounding his entire face and head. (01:16:50)
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)
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: 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 Lynn says "Please, please let me go" there are tears in both eyes and tear marks on her cheeks. 2 shots later (maybe 7 seconds) you see a close-up of her face and there are no tears or tear marks. (Jigsaw was holding her hand, so she couldn't have wiped them away, plus you can see Lynn the whole time (in the background) and she never wipes them off). (01:26:10)
Continuity mistake: Jeff lays his bloodied hand right in the center of Jigsaw's chest (pointing towards Jigsaw's chin) when he says "I forgive you", but pretty much only his fingertips touch Jigsaw. Right before Jeff slices Jigsaw's neck you can see the handprint, but it's MUCH more defined than it should be AND the fingers are pointing towards the right instead of straight up. (01:42:10)
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.