Continuity mistake: When Adam and Gordon are talking in the beginning, Adam's hair moves between shots. (00:03:40)
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 Dr. Gordon picks up his tape, the way he holds it changes instantly. (00:06:50)
Continuity mistake: Dr. Gordon empties his envelope into his hands in an extreme closeup. In this shot you can see the tape is not sticking up. Camera changes and the tape is now sticking up. (00:06:50)
Continuity mistake: Dr. Gordon gets a key in his envelope. The way he hold it changes instantly. Note the straight edge. (00:07:10)
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)
Continuity mistake: The mark on Larry's face changes throughout the film. (00:12:30 - 01:08:45)
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: Adam swishes his hand in the filthy toilet, getting brown liquid over his hand. Adam's hand suddenly becomes completely clean a very short time later. (00:12:50)
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: When the victims first find the saws and are vigorously trying to cut the chains: The wide angle of Larry sawing, shows him cutting at the chain. Close up he is cutting the padlock. (00:14:20)
Continuity mistake: During the quick montage of Adam and Lawrence cutting their chains, in one shot of Lawrence his feet are on white tiles and in others they are on broken sections that are black. (00:14:25)
Continuity mistake: Adam's hacksaw blade snaps almost as soon as he gets it. However, later on (just after he gets electrocuted) we see it lying beside him with the blade in one piece. (00:14:30 - 01:03:30)
Continuity mistake: When Dr Gordon is called to his office to speak with the two detectives, his chair is facing away from him as he approaches it but it suddenly turns, so he can sit down and talk with the detectives. (00:20:20)
Continuity mistake: We see Adam on Dr. Gordon on the screen that Zep is watching. By Adam's foot there is nothing, yet when we see Adam, there is a piece of glass. (00:30:00)
Continuity mistake: When we see the bathroom again after we hear about Amanda, the clock is at 11:35. When Adam breaks the glass, just a few continuous minutes later, the time is 12:20. (00:30:00)
Continuity mistake: When Adam finishes throwing stuff at the camera and Dr Gordon explains about every angle being thought out, the shard of glass at Adams feet keeps changing position without being touched. (00:30:40)
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)
Continuity mistake: Tapp is watching the Amanda tape. Jigsaw says "look" and then Tapp rewinds the tape for 2 seconds. He presses play and Jigsaw says, "Look around" He should have said the word "mate" at that point. (00:43:40)
Continuity mistake: When Tapp and Singh work out where the warehouse is Tapp has his hand out on the table over a map. The camera cuts and now they're on the arm of his chair. (00:44:50)
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.