Continuity mistake: When Dr. Lawrence opened his envelope he got a key in it. When he tried it on the lock on his chain and it failed to open, Adam then asks to try it. Right when Adam asks for it, he puts his tape and envelope down separate, but when reaches for his tape again, it has ended up inside the envelope. (00:07:50)
Audio problem: When Dr. Gordon is dialing 911, we hear one low tone then two higher tones. On touch-tones phones, 1, 4, and 7 are the lowest tones while 3, 6 and 9 are the highest. Gordon would have dialed a 1, 4 or 7 first and then a 3, 6 or 9 twice in succession. Possibly 1-9-9 for Emergency? (00:55:50)
Continuity mistake: When Dr Gordon is going crazy, he throws the box to his right, but in the next shot it's on the left, then on the right again. (01:25:50)
Continuity mistake: When Dr. Gordon gets out of Tapp's car and is talking to him at the car window, the amount of shirt sleeve showing under his jacket changes between shots. (00:42:00)
Revealing mistake: When we see Paul walking round the room with glass on the floor, if you look carefully you can see he has shoes on in some shots. (00:19:15)
Visible crew/equipment: Just as Adam shouts "Somebody help me" right at the very start, you can see a boom shadow move over the wall. (00:01:30)
Continuity mistake: When we first see the heart on the toilet, the lid is on upside down. When we see Adam look at it, the lid is on the right way up. (00:12:35)
Continuity mistake: When Adam retrieves the bag with the saws from the toilet, he places it on his right side. At one point you can see that there is nothing on his left side, but the next shot shows Adam grabbing the bag from his left side and tossing it into the tub. (00:14:00)
Continuity mistake: Dr. Gordon rips open his envelope near the start. When he does he rips it with the "A" in "Lawrence" still visible. Camera cuts and the rip has moved down to take off half of the "W". (00:06:45)
Continuity mistake: When Adam is walking into his apartment, his camera has a short lens on it. He then rounds the corner and goes into the darkroom and the camera has a long lens on it. (01:04:20)
Continuity mistake: When Adam throws the picture that he found in Lawrence's wallet to him, the picture lands next to the rectangular piece of tile that Lawrence uses in the immediate next shot to bring the picture closer to him. The tile moves from in front of him (given it's proximity to the photo) to right beside his right arm/hand. It "moved" about two feet. (00:59:10)
Factual error: After the doctor speaks on the cell phone for the first time and the line goes dead, there is a dial tone. There is no dial tone on a cell phone. (01:09:30)
Continuity mistake: The mark on Larry's face changes throughout the film. (00:12:30 - 01:08:45)
Audio problem: When Larry goes out into the hall after seeing to his daughter, Ally starts to talk to him but her mouth doesn't move with the words.
Audio problem: Adam throws a very small object at the mirror with his second throw. Yet the sound is of something a lot bigger hitting the glass. (00:29:35)
Continuity mistake: Dr. Gordon gets a key in his envelope. The way he hold it changes instantly. Note the straight edge. (00:07:10)
Revealing mistake: In the scene when Zep arrives in the room and Lawrence is trying to grab at him, his foot is no longer leaving a blood trail. (01:29:45)
Character mistake: Detective Sing asks Dr Gordon to listen to Amanda's testimony. Any detective would know its not a testimony, its a statement. Testimonies are done in court, not a police station. (00:23:00)
Continuity mistake: When Dr. Gordon is trying to get the phone it is just mm away from the box. When the camera changes, it's a good few inches away from the box. (01:25:05)
Continuity mistake: When Ali is pointing the gun at Zep, she is either holding it in her left hand or two-handed at one point. This is not to be confused with when the gun swaps hands. (01:20:15)
Chosen answer: Yes. You pretty much guessed correctly. We can assume that Jigsaw told Zep to tell Ali to tell Dr Gordon, "do not believe Adam's lies..." Don't forget that Jigsaw spends hours planning his tests so it would be safe to say that he had planned it all in the beginning.