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.
Revealing mistake: During the opening trap, at one point one of the five "Bucket Heads" starts banging on the wall behind them. If you look very closely, you can see the set-wall waver slightly as it's struck, revealing it's not really a concrete wall. (And it's not supposed to be the doorway that is later revealed during the final twist. It's a separate section of wall). (00:05:40)
Other mistake: During the opening trap we see Mitch strike the blades with his chain and get yanked forward. However, despite being yanked forward he still manages to stand in line with the others which he shouldn't be able to do, as his chain was shorter due to the extra tug he received. (00:06:30)