Well dude, I have to be honest.
If I had the time to fix it I most definitely would, but you have problems spawning from poor modeling. I know this may not sound very nice, but let me explain. I cleaned up the verts you were having problems with and when I moved the bones I realized that there is so much overlapping geometry on your model. So I tried to do a quick cleanup, and well it revealed many time consuming problems. The geometry cleanup removed lots of unnecessary faces, but you have so many unconnected verts, incorrect faces, and weird normals.
In the attached picture you can see a brief example of what I found. In fact maya just crashed as I was trying to clean up some of the geometry for you. Not a good sign.

I'd honestly recommend practicing your modeling skills, and re-doing the model. This would probably take less time to remodel than it would to fix. The biggest issue here with the jaws is that they look like they were made of objects separate from the body, and they all need to spawn from one object or such issues occur.

There are issues I see with the rig, but I don't see them as giving you problems, but it is the mesh that needs a fix.