Continuity mistake: Saw VII takes place straight after Saw VI. In Saw VI we see Jill put Hoffman in the bear trap and leave. We then see that Hoffman spends around 45 seconds trying to get the trap off before putting in the bars on the window. In this film however, just after Jill closes the door we see the glass break. No delay. (00:08:20)
Visible crew/equipment: When Hoffman runs to hide from the second coroner, he goes right up close to the camera. When he does, you can see the camera's shadow on his face. (01:08:00)

Continuity mistake: The amount of blood on Bobby's teeth constantly changes. During the tooth room (01:02:00)
Visible crew/equipment: When Hoffman is strapping Jill's second wrist into the chair, look at his head. As the camera moves in for a closeup, you can see the camera's shadow move over Hoffman's head. (01:15:15)
Revealing mistake: Just before Hoffman knocks Jill out, there is no blood on her head or the table. As he grabs her head blood appears on her head just before he smashes it on to the table. (01:14:40)
Continuity mistake: When Bobby gets the tooth room, there is 19:55 left on the clock. There is a cut to the TV showing Joyce lasting 3 seconds. The countdown now still shows 19:55. (00:57:20)

Deliberate mistake: If you look at the IP address of the junkyard, it is listed as: 634.634.99.234.88. An IP never goes over 255. (01:00:10)
Factual error: Bobby extracts two teeth to get the combination to the next room. When he looks at the teeth, the numbers are on the tooth root. To do this would be impossible without removing the teeth first. (01:02:05)

Continuity mistake: During the public saw trap, when Brad is clipped by the saw, you see blood on the edge of it. However, when the angle of the camera changes, the saw is clean. When the angle switches again, there is blood on the saw. (00:05:55)

Continuity mistake: It is visible that Dr Gordon's handwriting when he writes " I know who you are", is different from the handwriting in Hoffman's letter. (01:19:40)
Continuity mistake: At the start we see the purple jacketed skater stop and look at the display. The red jacketed skater stops to the left of the purple one. Camera changes to a view from inside the display and the red jacket is now to the right of the purple one. (00:02:20)
Continuity mistake: Bobby extracts 2 teeth to get into the final room. When he's inserting the hooks into his chest he screams, revealing one of the teeth he pulled is back in place. (01:01:15 - 01:10:00)
Revealing mistake: When the door slams shut on the SWAT team, watch the wall. It wobbles. (01:09:10)
Continuity mistake: Jill stabs Hoffman in the neck. But when we see him looking for her there is no mark on his neck. (01:11:10)
Continuity mistake: The position of the pliers for Bobby to pull his teeth changes instantly. (00:58:00)

Continuity mistake: When Bobby is swinging from the cage near the start, the way he is holding onto the cage changes instantly. (00:31:40)

Continuity mistake: Brad gets blood all up his face when he is hit by the saw. When Ryan and Brad decided to let Dina die, the blood has gone from Brads face. (00:06:40)

Revealing mistake: Most of the blood seen in this film is too light to be considered real human blood. In the public trap it is practically pink. The reason for this is the 3D effect. When watched in 3D, it looks more like normal blood. But in normal viewing, it does look too light. (00:06:00)

Visible crew/equipment: When Bobby grabs the key for Cale's noose. There is a shadow on the door of a boom mic. (00:53:50)
Continuity mistake: Det. Rogers spots the note for Gibson from Hoffman and the reverse bear trap. When he calls Gibson over, he has his arm up and resting on the door frame. When Gibson looks into the room, Rogers lifts his arm again. (00:28:30)
Answer: He, his wife and his daughter were abducted before he decided to work with Jigsaw. He didn't put them in danger. As for why he decided to work with Jigsaw following his ordeal, like other characters in the franchise, he either developed a level of Stockholm syndrome or he concluded that Jigsaw's methods were right, or a combination of both.
Phaneron