Plot hole: Spoilers. It's revealed that the barn game takes place at an old farmhouse owned by the family of Jill Tuck - Jigsaw's widow. It's public knowledge that she was married to Jigsaw and that buildings they owned served as the headquarters of several past traps, so the barn should have been investigated at some point in the meantime. Ten years have passed. It makes no sense that the barn was never investigated and that the bodies of the barn victims were never discovered.
Plot hole: An order is given for the body of John Kramer to be exhumed. Surely the police would have noticed someone had dug the grave up in the last few hours (days at a push) as Logan had to get Munsen's body into John's casket.
Plot hole: Jigsaw is apparently omniscient - he was able to correctly identify all the sins of his victims even though he couldn't possibly have been there when they occurred.
Suggested correction: As we have seen throughout the franchise, Jigsaw has several servants who prepare traps for him and such (known as "Pigheads"). They would have been present at the time.
I don't know about this; Carly, for example, stole a purse with $3.53 in it. There is no way even the Pigheads would know that amount or be able to connect it to the death of the woman she robbed. In addition, if they were there to witness that specific crime, they easily could've saved the woman too.
Suggested correction: The game was unknown to police even 10 years after John died. Now they've found all his other games and his multiple lairs. There would be no need to continue the search.
Hogwash. They would have definitely searched known properties associated with Kramer and his family.
I agree. In the second Saw movie, the police discover that John Kramer is Jigsaw. With this knowledge, not only would the police be able to freeze his assets but, they would be able to look into his financial records and look into any properties he owns like houses, warehouses, etc. Since the cops now have a face and a name, it's a very big plot hole why they never searched his home or any other places. If they had, more traps would have been found and confiscated.