When the camera moves from Troy's crime scene to Kerry being in the bathtub, that was all one shot - Dina Meyer had to run around the set, take off all her clothes, and jump into the tub. If you look closely, you can still see the water moving from when she got in. See more...
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When Lynn says "Please, please let me go" there are tears in both eyes and tear marks on her cheeks. 2 shots later (maybe 7 seconds) you see a close-up of her face and there are no tears or tear marks. (Jigsaw was holding her hand, so she couldn't have wiped them away, plus you can see Lynn the whole time (in the background) and she never wipes them off).
In the 'Pig Vat' scene, the slide that the pigs slide on into the blades is clear with no pigs stuck on it. The pigs fall in one after the other with none getting stuck on the slide. However when the fourth pig drops onto the slide, you can see the a pig stuck on the slide and hanging over the edge of the slide. The next couple of pigs that fall don't knock another pig in and you cannot see the pig overhanging on the slide.
When the movie opens, Eric is in the bathroom and looks over at Adam, who is leaning up against the wall. However when we see Adam in Saw 2, he is propped up against the pipe. Eric hasn't moved him, as he's chained up. Obviously when they set up the bathroom for this movie, they did not put the dummy Adam in the same place.
Jeff lays his bloodied hand right in the center of Jigsaw's chest (pointing towards Jigsaw's chin) when he says "I forgive you", but pretty much only his fingertips touch Jigsaw. Right before Jeff slices Jigsaw's neck you can see the handprint, but it's MUCH more defined than it should be AND the fingers are pointing towards the right instead of straight up.
When Amanda says "I'm standing right here" her hair is hanging down, but brushed back from her right eye, in the previous and subsequent shots her hair is hanging down and covering her right eye. She was holding the gun in her right hand the whole time and all the cuts were instant, there was no time to move her hair.