I changed the origin of my skeleton, and nothing happened at first so I positioned the character as I wanted. But when I advanced the keyframes, it completely messed up the character's mesh and I can't go back far enough to fix it. changing the origin back didn't help. I made some progress trying to manually position the character inside the armature, but it would be very tedious to get it just right. The last time I saved a backup was before I started animating, so I would prefer if this could be fixed.
This probably is caused by the fact that you moved the character and not the rig. When the character is rigged, move it using the rig.
The root of the problem is that the Jonesy character is made up of different objects whose origins are in different places, including the skeleton. So when you animate the mesh travels and distorts.
Setup your character the way he is supposed to look above the ground plane and at the center of the world (X,Y,Z 0,0,0). Then, reset the 3D cursor Shift+C and in the Tools panel (pressing T) find Set Origin > Origin to 3D Cursor
After that, your meshes will stay in place when you animate.
I would also suggest the Humane Rigging Video Tutorials to help you with the rig ;).