Deliberate mistake: When Agent Hoffman writes the letter to Amanda, he puts the envelope so her name is pointing down, yet when Amanda opened this drawer in Saw III her name was at the top. The director had to do this or it would have revealed Hoffman was the new apprentice all along.
Deliberate mistake: When Randy is playing with Agent Rodriguez's gun (after first meeting him), when he accidentally fires it, you can tell the film inexplicably cuts forward a few frames into the same shot, as Randy's body suddenly shifts position and the gun is facing upwards, rather than at an angle as it was the frame before.
Deliberate mistake: At the end of the movie, where the girls chase stuntman Mike, they drive the upper dusty road. When their car is shown front outside angle, there's a lot of dust rising from the camera crew's car. But when the camera angle gets into their car and shoots strait ahead - the dust is all gone, the air is perfectly clear.
Deliberate mistake: In the facial morph, the faces don't come anywhere close. The face was morphed with no feature of either resembling the other. The only matching features were the hair and neck which were not touched by the morph. The midpoint of the shift wreaks of Photoshop-like effects (softening of the face alone). (00:41:50)
Deliberate mistake: The floating contact mine that explodes at the end of the movie would never have been put in an evidence room in a police station. Barring that error for the plot's sake, FCMs weigh 450lbs and would have required a hydraulic crane and a cart to move it, not just a couple of guys. They also did not contain clocks. (00:42:40)
Deliberate mistake: After Bert is shot in his car, Bobby pulls up beside him and just after Bobby shouts, "Pop, pull over!" the first time, the next tight close-up of Bobby's face is a flipped shot. Note his earring and the scar on his upper lip have switched sides. (01:17:00)
Deliberate mistake: When John crashes the car against the elevator room, the cables he and the woman hold on to are clean, when they should be greasy - thus allowing for them to hold safely.
Deliberate mistake: A stunt double for 47 got hurt on camera and yelled, very obviously. Right after the sword fight on the train the last man 47 is fighting continues the fight hand to hand under the tracks. Timothy Olyphants stunt double throws a punch and he grips his hand, yells and his face comes into screen for a moment. Next shot, Timothy Olyphant throwing his own punches.