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)
Revealing mistake: When Adam is searching Zep for the key to the chain once he has found the tape recorder watch Zep's stomach - he's breathing. (01:32:15)
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)
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)
Revealing mistake: In the scene when Zep arrives in the room and Lawrence is trying to grab at him, his foot is no longer leaving a blood trail. (01:29:45)
Revealing mistake: Adams shirt is dry, after being in a tub full of water. (00:10:20)
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)
Revealing mistake: The cut on Tapp's throat is visible a split second before his throat actually gets slashed. (00:49:50)
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.