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: The bloody handprint on Lawrence's shoulder that Adam makes at the end is visible before he actually makes it. Second, when Adam finds the tape recorder, it flashes back to Lawrence saying "why?" before Zep tells him it's the rules and the handprint is also visible, but shouldn't be there as Adam made it after he killed Zep. (01:29:40 - 01:33:10)
Continuity mistake: The bloody bullet wound is seen on Tapp after he's shot. When he is shown after he falls on the ground, the bullet wound is not there. (01:27:50)
Continuity mistake: When Adam takes the picture of Lawrence in the car park, the position of Lawrence's fingers on his face vary between the picture Adam took to the actual shot of him when he does so. (01:11:15)
Continuity mistake: When Singh is following Jigsaw, he shoots him in the back and proceeds to close in on Jigsaw. In one shot from behind him he is next to a wooden spool. Camera changes to in front of him and now he's further away. (00:51:20)
Continuity mistake: When Dr Gordon is breaking the wall to get the box, there is 1 tile at the top that is complete on the outside shot and broken on the inside shot. (00:54:10)
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)
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)
Other mistake: When you see the shot of the camera watching Adam and Dr Gordon, you can see a plank sticking out directly in front of the camera. A little later, when you see the camera's view, which has some incredibly wide views, you can't see the plank, which would definitely have to be visible to see both of the people in the bathroom. (00:29:40)
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: 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: 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: When Dr Gordon is reading the note that was in the box with the phone, the way he holds it differs between shots. It goes from 2 handed to single-handed. (00:55:50)
Revealing mistake: When we see Tapp watching Dr Gordon's house, there are clips of newspaper headlines that flash up on the screen. However, the articles themselves have nothing to do with Jigsaw or even the headline above them. (00:41:00)
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 and Gordon are talking in the beginning, Adam's hair moves between shots. (00:03:40)
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.