[GRIZZ]

That can't be right: the killer in this one is shown at the end, and it's the detective, so why would it show him finding a tape in present time telling him to carry on the work if he already was carrying it on?

I agree because that is the way I saw it. At the beginning it showed the tape in Jigsaw's stomach. Then it flashed back some parts to show why some events were currently taking place. It wasn't that hard to follow as long as you have seen the second and the third one.