Continuity mistake: Just before Amanda shoots Lynn her gun switches from her right hand to her left.
Continuity mistake: Lynn is in the corner of the room when Amanda is threatening her with the gun. The shot moves to behind Amanda when she raises her hand to her head and now all of a sudden Lynn is a good 4 or 5 feet to her right. (instant cut, not enough time to move).
Continuity mistake: The glowing "X" on the bathroom wall in the first Saw movie was very symmetrical, and the whole thing was filled in very well. During the Saw III bathroom flashback scene, when Jigsaw paints the "X" it's completely different that the one that shows up in Saw. It's not symmetrical at all, and the paint doesn't go on very thick at all. You can easily still see the wall behind the paint, but in Saw, the lines of the "X" are very full with no gaps.
Continuity mistake: Jeff sees the 3rd tape player (in the room where he finds the judge) and there's a shot of the player being held up by string. The player is hanging very level and the string is perfectly tied around the middle of it. Jeff climbs the stairs to get the player and now you can see that the player is hanging crooked and the string (where it's tied) is slanted towards the top of the player. (He didn't shake it lose or anything when he climbed the steps, the player is hanging from the ceiling).
Continuity mistake: When Jeff leans down to Lynn you can see she she has some blood on her chin and neck. The shot goes to Jigsaw, then back to Lynn and Jeff. Now her neck and chin have no blood. Shot moves to Jigsaw again, then back to Jeff and Lynn. Now she has blood on her neck and chin *and* blood from the corner of her mouth.
Factual error: Troy has several chains attached to his body, of which two are attached to his Achilles tendons. This is the structure of the leg that allows you to stand and move, so as soon as he ripped them out, he would have fallen over and been unable to walk.
Revealing mistake: During the "Rack" trap, look closely whenever there's a close-up of any of Timothy's hands or feet. It takes careful observation, but you can tell that many close-up shots have been horizontally flipped during editing. This was because the production only spent money on one prosthetic/prop hand and one prosthetic/prop foot for the twisting/bone-breaking effects, and in order to make it look like all four of his limbs were breaking, shots would be horizontally flipped. Thus the same prop/prosthetic could serve as both the left and right hand or foot. What gives it away is the blood pattern on the foot, which is perfectly mirrored between his two feet.
Continuity mistake: After Lynn gets shot her position against the wall changes between the far away and close-up shots. (look at the poster she's leaning against for a reference point, in the far away shot her head is between the 2 legs on the left, but in the close-up her head is on the very left leg and you can easily see the right leg.).
Continuity mistake: The blood spots on Jigsaw's hospital bed disappear during shots of him telling Amanda to let Lynn go, and they reappear in later scenes.
Continuity mistake: When Jeff is screaming at the guy in "The Rack" there are a few spinning shots of "The Rack". You can see that the guy's arms aren't broken, even though you've seen them both be twisted until they snapped. (Slo-mo helps but is NOT required).
Revealing mistake: Notice that throughout the movie the primers (little 'buttons' on the tips of the shotgun shells) on Lynn's neck trap have all been expended. In a sense, none of the shells have the capacity to be fired.
Continuity mistake: When Amanda says "I'm standing right here" her hair is hanging down, but brushed back from her right eye, in the previous and subsequent shots her hair is hanging down and covering her right eye. She was holding the gun in her right hand the whole time and all the cuts were instant, there was no time to move her hair.
Deliberate mistake: In Saw III we learn that Amanda was the person who abducted Adam from his apartment. However, if you watch his abduction in the first Saw film, you'll see that the person attacking him has the hands of a middle aged man.
Continuity mistake: The green tube that's connected to Jigsaw is gone when he says "Suffering? You haven't seen anything yet", but it was there in the previous scene and it's back the next time you see him.
Continuity mistake: Amanda's holding the gun in her right hand in every scene when she's arguing with Jigsaw, except when she's saying "It's all BS," then the gun is in her left hand. It's back in her right hand then very next scene (all instant cuts, no time to switch hands).
Continuity mistake: Amanda's hair is in a lose ponytail when she sees Jigsaw holding Lynn's hand. A large part of her hair is hanging down the right side of her face and in her eye. She storms out of the room and now all of a sudden her hair is all pulled back in a tight ponytail and no hair is hanging down or behind her ear, it's all back in the ponytail (instant cut, no time for her to re-do her hair).
Continuity mistake: When Jeff is monologuing about how "Everyday for 3 years I wanted to kill him" there is a tear that appears in his right eye and starts to run down his cheek. The shot cuts away for a second, then back to Jeff and there is no tear, not even a wet tear trail.
Continuity mistake: There's a shot of the right foot when "The Rack" starts twisting it. There is a blood trail that runs off between his first 2 toes, and a lesser one that runs off between his 2nd and 3rd toes. The screen cuts to a close-up of the foot and there's only the blood trail that runs off between the first 2 toes.
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.
Visible crew/equipment: Just before Amanda shoots Lynn, a mini microphone can be seen on Amanda's neck. It is only visible for a few seconds then vanishes, so look quickly.
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.