For the inside of the mouth you need to merge the vertices there while in poly mode that willg et ride of the problems younare having. Also to stop the problem in the future in maya go to polygon> tool options and select keep faces together. This will keep all the faces together when you extured and you will not have to merge them any more.
I am enough of an artist to draw freely upon my imagination, knowledge is limited, imagination encircles the world. (Albert Einstein)