Continuity mistake: When the movie opens, Eric is in the bathroom and looks over at Adam, who is leaning up against the wall. However when we see Adam in Saw 2, he is propped up against the pipe. Eric hasn't moved him, as he's chained up. Obviously when they set up the bathroom for this movie, they did not put the dummy Adam in the same place. This scene takes place immediately after the scene in Saw 2, and thus there's no time for the body to have been moved at all. (00:00:50)
Continuity mistake: Matthews is in the bathroom and gets the saw, he shines the light over and sees the severed foot on the other side of the room. He shines the light down to his foot, then he holds the flashlight in his mouth while he yanks his sock off. The next shot (which is a direct cut, you can tell by his sobs) has the flashlight suddenly on the floor and already pointing at his foot while he's stuffing the sock in his mouth to muffle his screams. (00:02:00)
Continuity mistake: Watch the light when Matthews is breaking the bone so that he can slide his foot out of the lock (right after he's done smashing it with the lid). The flashlight is suppose to be on the floor next to the foot (it was in the previous shot) but the light source is moving all around as he places his hands on his foot and then breaks it. It's very noticeable as soon as the break happens, the light source moves down and to the left of the screen. The flashlight is back on the ground, next to the foot, in the very next shot. (00:02:10)
Continuity mistake: The placement of the flashlight (or foot) moves between shots of Detective Matthews contemplating sawing through his leg. In one shot the flashlight is illuminating the ball of his foot, in the next it's pointed past his foot, then in the next shot it's shining right on his heel. Matthews isn't moving either, he sitting right there with the saw on his leg, crying and contemplating all the pain that he's about to inflict on himself. (00:02:30)
Continuity mistake: When Matthews is smashing his foot with the toilet bowl lid, he probably hits his foot a good six or seven times, and one of the times he also glances against the flashlight and it rolls a bit to the side. The next time you see the flashlight it's pointed right back at his foot like it was in the previous shots. (He was still pounding away on his foot, so he didn't stop and realign it or anything.) (00:03:00)
Continuity mistake: There is a closeup shot of Matthew's foot right before he starts to smash it with the broken piece of the toilet bowl lid. He's placing the flashlight on the floor next to his foot and you can see that the sock is back on his foot, even though he took it off previously (right before he first attempted to saw through his leg). (00:03:20)
Revealing mistake: When Eric Matthews is smashing his foot, he hits it the first time and it shows a close up. If you watch the small amount of blood when he hits it again they have used the same shot. (00:04:00)
Revealing mistake: Look at Matthews' toes as soon as he's done breaking his ankle, it's obvious that it's a fake foot. If you shine a flashlight through your toes, or fingers, it will shine most brightly through the edges of them because in the middle there's a bone to block the passage of light. The light shines right through Matthews' toes, and it's a solid color, obvious that there's nothing inside to block the passage of light. While he did break several bones in his foot to escape, it is unlikely that he took time to break his toes as there is no reason to, the shackle will slide off unbroken toes as well as broken ones. Also, even if he did break his toes, the broken pieces would still be in his foot and still block the light. It's a fake foot. (00:04:15)
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)
Continuity mistake: The blood spots and streaks on the chained man's body are different in the close up shots of the chains than they are during other shots. (00:06:00)
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)
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: The guy that is in chains stands up, looks around and takes in what he sees. There's a shot of him from the front and his hands are semi-clenched in FRONT of him, around waist level. The shot cuts to behind him and his hands are a good 4 or 5 inches OUTSIDE of his hips. (00:06:35)
Continuity mistake: There is a shot when Tony (chained man) is listening to Jigsaw's message where blood drops out of his mouth and runs down his chin, but in the next close-up of Tony you can see that most of the blood has mysteriously disappeared (he still has blood on his chin, but it looks the same way that it did BEFORE he drooled blood all over the place). (00:07:30)
Revealing mistake: After Tony rips his right hand from the chain you can see that the wound doesn't go all the way down to between his fingers, it stop about 1/2 an inch from the webbing of the fingers. The only way to get the chain out oh his hand was to completely rip it out between his fingers, the wound should have gone all the way out. (somewhat difficult to see, but just look carefully [slow-mo helps, but it NOT required to see this mistake]). (00:08:40)
Continuity mistake: When Rigg is telling Kerry that "That somebody is still out there", Hoffman can be seen in the background putting something in his jacket. Camera changes and his hand is nowhere near his jacket. (00:10:00)
Continuity mistake: After the scene of Tony there is a shot of Kerry and Rigg, the detective is in the background inspecting a piece of the chain. The shot moves to the background detective for a second and he looks up at something. The shot instantly cuts back to Kerry and Rigg and the background detective is suddenly looking down at the chain again. (00:10:25)
Continuity mistake: When Kerry is talking to Rigg and the detective she is almost directly in front of the door. When the other girl says "You won't believe this, we got the tape out clean" the camera pans around and you can see that Kerry is now in front of the chalk boards. (00:11:05)
Continuity mistake: Kerry wipes off the steamed up mirror and sees Eric in the reflection, she gasps and turns around. She looks back at the mirror and you can see that the hand wipe marks where she wiped the steam off are completely different. (00:11:45)
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)
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.