The son asks his mother why they could be trapped in the acid cage, and the mother angrily replies, "We're here because of your father!" His father is Harold, the man who was denied a claim by William; not William as the movie leads the audience to believe. Therefore, her angry line about "your father" makes no sense.
When Hoffman's glass coffin ejects from the 'crushing room', his face is visible. However, in the flashback footage from Saw V, Agent Strahm's blood spatters further across the panel, hiding Hoffman completely from view.
When Hoffman raises the lid to the glass box after escaping the Crushing Room, the blood remains on the lid in a fixed pattern, showing it is dry, even though it was only spurted on to it seconds before.
When the coroner is talking to Hoffman and the Feds, he says that the knife used to remove the jigsaw piece from Eddie had a partially serrated edge. The coroner then claims that same knife was used to cut the jigsaw piece from Seth Baxter. However, in Saw V you can clearly see that the knife used to remove the jigsaw piece from Seth Baxter is a non-serrated scalpel, not the "knife with a partially-serrated edge" that the coroner claims was used.
(at around 30 mins) When Simone is in the hospital, and Detective Hoffman visits her, there is a hand on her shoulder in the "close up" view to clam her down after Hoffman asks her if she "learned." However, when the camera zooms out a few seconds later, the nurse is just then going up toward her, to put her hand on Simone's shoulder.
During the footage of John Kramer when he is ill and apparently going through chemotherapy, he quite clearly has a small, thin beard on his chin. Chemotherapy kills rapidly dividing cells, such as cancer cells, hair cells and fingernails. It would be impossible to grow facial hair when going through this therapy.
John Kramer says he doesn't care about the cost of surgery since he is very wealthy. However, when his insurance claim for an overseas treatment is denied by William, he seemingly forgets this fact. He simply derides William and just accepts defeat despite the fact that he, by his own admission, could afford to just travel overseas and receive the treatment anyway. Furthermore, why would John, who in a flashback castigated William for his immoral business practices, take insurance from him in the first place?
During the Steam trap, the trajectory of the trap is completely off. When it fires, it is shown entering her neck, but a couple seconds later it is seen sticking out of her skull above her left eye. It should either have gone through her neck and out the back, or sticking out the back of her head instead.
The goof items below may give away important plot points.
Jigsaw's entire modus operandi is predicated on the idea that the person being forced to play his game learns something and changes their life. William is forced to go through one of Jigsaw's games, and he definitely changes; however, it turns out that he didn't have any control over his fate after all because Harold's son simply kills him at the end of the game.
At the end when William is dissolved by the acid, the trap swings from the ceiling pinning him against the metal cage wall. From the look of it, the trap leaves close to 2 - 2 1/2 feet from the ground open and doesn't even touch the other side of the cage near his wife. All he had to do was either duck, or stand near his wife and he would have been completely safe. Unless Hoffman predicted that Will would be pleading for his life instead of being close to his wife in his last few minutes, it doesn't make sense why the trap would be rigged that way.