@ben I think this lecture needs revisiting.
I and, judging by the topics in this discussion, a significant portion of other students have absolutely destroyed their rigging and animation by following your steps. The mesh explodes all over the place when applying the modifier or playing the animation. I have managed to rig the new mesh but had to delete the animation which is a pain since it took me all day yesterday to create it.
I think it has to do with applying Loc/Rot/Scale and the origins of the mesh objects and the armature before re-rigging but i couldnt figure it out to save the animation.
Please do include a section to explain and fix this problem!
[Edit] @Mobilephoria @ben and for everybody reading this in search for answers: apply Rotation/Location/Scale to all mesh objects before joining them into single mesh. worked for me.