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: 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: When Adam pounds on Zep with the toilet seat, he grabs his shoulder in pain. In the first shot of him holding his shoulder, his hand is soaked in blood. In the second shot, however, his hand is much cleaner. (01:30:25)
Continuity mistake: Jigsaw's thumb moves between shots after Adam gets the mini cassette recorder out of his hands. You can see Jigsaw's thumb, in the closeup shot, slide down to a position where it's lying horizontal and flat on the floor as the mini cassette recorder is being slid out of his hand. In the next shot, an overhead, you can see that his thumb has moved and is now more curled and in a more vertical position to where just the tip is touching the floor. Jigsaw isn't dead, so he could have moved, but this shot is an *instant* cut, he had no time to move.
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.