Try smoothing the mesh. That's the problem 
That my friend is defo the thing NOT to do on a model where the geo is a mess. - I am little shocked this came from NextDesign as his work is usually quite strong, and alot of the other stuff he talks about in his replies is correct and makes sense, just not that bit.
Now that you found the "split poly tool" use it to clean up the mess - what you want is to make all the polys 4 sided. You can also do this by deleting some edges. Have a look at the image I have added - This is what it should look like if you were to add all the extra lines in. I would use a bit of both ( add and delete) as long as they are all quads your good to go. (Edit - just noticed I did miss a few lines on that image but you get the idea)
Daverave has shown you a good way to make the jaw - but if you still want the mouth separated and angled what you need to do is.
1) Select the faces you want
2) Make sure your in the "Polygon" tab
3) Then Select - Mesh > Extract - this will separate the lower jaw for you. My bad using the word detach in my last post - wrong word but correct discretion if you get my meaning there.
4) Select lower jaw and "Edit > Delete by Type > History"
5) Then "Modify > Centre Pivot"
6) Press Insert to change the pivot placement to the end of the Jaw. You can do this manually or snap it.
7) Press Insert again and rotate it to the angle you want
8) Select the vertex`s and snap then to the upper jaw so it matches up into the model.
9) Select both and "Mesh > Combine"
10 Fill in the inside of the jaw by iva "Create polygon tool" or "Extrude edge".
FYI - Booleans are fine to use if you know what your doing - I use them all the time to make holes in things. The biggest trick is to start low poly then work up, but many peeps hate them because they cant use them. They even better in Maya 2015.
Hope this helps
Last edited by tweetytunes; 14-04-2014 at 09:30 PM.