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 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)
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: 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: Adam grabs the bat with both hands right after he sees the laughing doll in his apartment (the view is from behind him). The very next shot shows the front of him, but he has the bat in one hand, and the camera in the other. (01:07:10)
Revealing mistake: In Adam's flat just as he starts beating Jigsaw's doll (Billy) up, you can see that he's not actually hitting the proper puppet, but a cheap replica. You can tell by the red lines on it's face, and there is no red marks where it's mouth is. (01:07:30)
Visible crew/equipment: In the scene where Adam walks around his apartment with his camera (because the lights were out) the filmmakers put lights in the set so the actors wouldn't walk into walls, and also letting the audience see what's actually happening. In the movie, though, there are supposed to be no lights on at all. However, just before Adam opens the closet door with Jigsaw in it, you can see the reflection of one of the set's lights on the top of Adam's camera. (01:07:40)
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: 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)
Other mistake: When Adam is saying to Dr. Gordon "What I saw was you get into your car, that's it," Leigh Whannell's natural Australian accent slips through on the last two words. (01:18:09)
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 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)
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 Alison is pointing the gun at Zep, Zep's position in relation to the bed changes instantly. (01:20:50)
Continuity mistake: In the car chase scene, Zep is seen driving a late 80's Ford Bronco II (could be a Ranger pickup because we only see the front). When he arrives at the warehouse, the truck has changed to an early 90s Ford F-150. (01:23:40)
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 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: 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)
Factual error: While Dr. Gordon is sawing off his foot, he only has blood on his hands and some on his shirt. Since the blood on his shirt was from splatter, that means he must have cut through a few veins or arteries, yet he has no blood on his arms or face, which should certainly happen when cutting through something like that. (01:26:30)
Continuity mistake: When Dr Gordon begins to saw his foot off, the blood seen covering his neck and top disappear in subsequent shots. (01:26:40)
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.