Revealing mistake: After Dr. Lawrence cuts off his leg and is crawling towards the gun, if you look at his dismembered leg, you can make out the shape of his foot hidden beneath his ripped up slacks. (01:29:30)
Continuity mistake: When Dr. Gordon picks up his tape, the way he holds it changes instantly. (00:06:50)
Continuity mistake: When Alison gets the gun from Zep and aims it at him, the gun is in her left hand. In the next shot it's in her right hand, and then it moves back to her left hand again. This is not an artifact of changing camera angles, you can clearly see the different hands holding the gun. (01:20:30)
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: When Larry is desperately trying to reach for the cell phone, he uses the box that it came in. When that doesn't work he throws it off to the side (his left) but when we see it again the box is back where it originally was (on his right). (01:25:40)
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 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: When Larry takes the box out of the wall, it turns itself around from when he's holding it, to when it's on the floor (keep an eye on the box's padlock). (00:54:50)
Continuity mistake: In the scene where. Lawrence and Adam find the 'X' on the wall, there is a continuity error. Right after they find the 'X', the lights are turned on and there is the shape of a square on the wall (the cavity where the box is hidden). Before they find the 'X' there is no box or any dirty lines where the cavity is. (00:54:00)
Continuity mistake: When Larry looks at the picture with Zep at the window, from one angle the picture is all crumpled but in the first person view, it's smooth. This changes several times. (01:18:40)
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)
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)
Continuity mistake: The mark on Larry's face changes throughout the film. (00:12:30 - 01:08:45)
Continuity mistake: When Tapp and Sing go to Jigsaw's place and find the guy strapped to the chair, they uncover him, then re-cover him to see what Jigsaw is going to do. When Jigsaw pulls the sheet off, one side is still caught on the drill bits. When he starts the drills the sheet is completely clear. (00:48:00)
Other mistake: When Larry is taking the cigarettes out of the box, look at his hand. It has a white paint drop or white dust on it, but throughout the scene it disappears and reappears. (00:55:10)
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.