Character mistake: Detective Sing asks Dr Gordon to listen to Amanda's testimony. Any detective would know its not a testimony, its a statement. Testimonies are done in court, not a police station. (00:23:00)
Factual error: The Swedish subtitlers made Amanda's situation even more tragic, incorrectly translating her dead cellmate as her dead soulmate. (00:24:40)
Audio problem: Adam throws a very small object at the mirror with his second throw. Yet the sound is of something a lot bigger hitting the glass. (00:29:35)

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: 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)
Visible crew/equipment: You can see the shadow of the camera on Dr. Gordon's sleeve when he is talking to Diana sitting on her bed. (00:34:20)

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 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)
Continuity mistake: When Tapp and Sing discover the Billy puppet in Jigsaw's warehouse, the puppet's head changes direction at least once. (00:47:10)

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)
Revealing mistake: The cut on Tapp's throat is visible a split second before his throat actually gets slashed. (00:49:50)

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: 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 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 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)

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.