Putting the mint box to one side for now, solder the electrical components together as per the wiring diagram. The idea is to get everything soldered before mounting it all the box. I used a DPDT switch and wired both the positive and negative through the switch. This isn't necessary electrically, but it keeps things tidy within the mint box. Use heatshrink tubing on the switch contacts to help with durability and reduce the risk of shorting out on the metal box. Make sure that the length of wire between the switch and the battery holder is longer than twice the length of the box (you may need to use extra wire and heatshrink tubing). This extra wire will make it much easier to pull the AA holder out to change batteries.
Obviously, since his flashlight doesn't explode every time he turns it on, he has wired it correctly.
The important thing is to be sure you wire your switch correctly.
Most switches, as far as I know, require both positive and negative connections.